StatsG0d

I agree with @bayessays. Most students will basically have taken up to Real Analysis and not much extra. Some students even get admitted without RA, although this is becoming more rare.
I do think that the more you have, the stronger your application will be. So if you're fighting for the top programs, it definitely won't hurt to take more math (provided you earn good grades in those classes).

I'm not sure if any Statistics program will specifically be a pipeline for federal jobs. I do know a few PhD alumni from different programs who have ended up at places like national labs (e.g. Los Alamos National Laboratory), as well as federal agencies and government-sponsored enterprise like the FDA, the NASS branch of the USDA, Department of Defense, and Freddie Mac. If you go to any Stat PhD program and you are an American citizen, then I don't think it matters a whole lot where you got your PhD. It is possible that your research area matters though. Some of the federal jobs require a "technical talk" as part of your interview, and if you have particular expertise in an area of interest to them, you could get hired just on that basis. For example, there used to be a professor at the department where I got my PhD who left academia to work as a Director of R&D at the NASS. I'm pretty sure this was largely because this professor's research focused a lot on spatial statistics and ecological/environmental applications.
I think maybe Biostatistics sends more alumni to certain types of federal jobs, e.g. at the FDA.

It's possible (and highly likely) that the other students had already taken the course (e.g., in undergrad). You definitely need to take real analysis for stats. You *might* be able to get away without taking it if you're doing biostats (although, this is becoming less common at the top 5-7 programs, as the field is becoming more competitive).
Even if you managed to get into a program without taking analysis, you would have wished that you'd taken it. Even in Casella-Berger level Math Stats, real analysis is very useful for making mathematically rigorous arguments / proofs. I feel like you (or anyone without real analysis) would struggle in a pure stats program without it.
Any/all of those courses will be useful when you reach the dissertation stage, but the reality is adcoms don't really care much about how many statistics courses are taken (unless they're mathematically rigorous courses e.g., linear models, probability theory, (martingale-based) survival analysis, etc.). If I'm on an adcom and I see that you've taken these stats courses, I'll think "OK, it's nice that they clearly have shown an interest in statistics, but how prepared are they to be successful in the program?" I'd look at the GRE and see a lower score relative to other applicants, and then think "well, perhaps this student had a lower GRE score, but has demonstrated mathematical maturity through courses." Then, when I see the lack of a single proof-based course on the profile, I would almost certainly reject the applicant. 
 
I think it's important for you to reflect deeply and see if you know what you're getting yourself into. If you are trying to avoid taking real analysis because you dislike theory, then I can assure you that you will not like doing a stats PhD, and you will burn out really quickly. The courses / qualifying exam is difficult even for those that have taken real analysis, and I truthfully can't imagine an individual doing well without it, especially relative to peers.
If you are more interested in the application of statistics, there are other fields you can consider that utilize advanced statistical methods (e.g., epidemiology, psychology, quantitative methods in the social sciences) without the need to dive into the theory. The purpose of a stats PhD is to make you equipped to develop your own methods.

I think you're selling yourself really short. First, I wouldn't bother applying to UCSD, TAMU, Rutgers, or Rice. NCSU doesn't have a PhD in biostatistics, although they do have a Biostatistics concentration in their Statistics department. Also, not sure if UW refers to Wisconsin or Washington.
You're competitive for any of the biostats programs in the top-5. In fact, I would be shocked if you didn't at least get into one of UNC or Michigan. I would say apply to all the top-7 biostats programs and maybe those Canadian schools if you're interested. I'd maybe add McGill if you're interested in precision medicine. I'd also add Berkeley if you're interested in causal inference.
It sort of depends. If you've taken all the qualifying exam courses, the department *might* let you take the qualifying exam the summer you arrive. Otherwise, they may force you to retake their versions of the courses and then take the qualifying exam at the end of the first year. It usually depends on both the department and the specific case.
If the qualifying exam is taken in the 2nd year (e.g., how it is at UNC), they'll let you skip the first year curriculum, but you'll have to take the 2nd year curriculum and take the qualifying exam the summer after your first year.

I agree if the OP meant stats departments then they should apply to those. I assumed they meant biostats 

I think you can apply to the top programs, but I think the top 3 will be hard to crack.  I agree with @StatsG0d that you should cut some of the lower schools off the list -- although TAMU, Rice, NCSU and Rutgers are very good schools if you mean their statistics departments and I think are good schools to target.  I think you should probably get into better programs than Pitt/Emory/BU/Columbia/UT-Anderson/Vanderbilt though, and you should cut these down to maybe only 2 of the above as safer options.  I think the biggest zone to be targeting will be Michigan/UNC/Minnesota/UPenn, with a few below and a few above.  

I think you're selling yourself really short. First, I wouldn't bother applying to UCSD, TAMU, Rutgers, or Rice. NCSU doesn't have a PhD in biostatistics, although they do have a Biostatistics concentration in their Statistics department. Also, not sure if UW refers to Wisconsin or Washington.
You're competitive for any of the biostats programs in the top-5. In fact, I would be shocked if you didn't at least get into one of UNC or Michigan. I would say apply to all the top-7 biostats programs and maybe those Canadian schools if you're interested. I'd maybe add McGill if you're interested in precision medicine. I'd also add Berkeley if you're interested in causal inference.
It sort of depends. If you've taken all the qualifying exam courses, the department *might* let you take the qualifying exam the summer you arrive. Otherwise, they may force you to retake their versions of the courses and then take the qualifying exam at the end of the first year. It usually depends on both the department and the specific case.
If the qualifying exam is taken in the 2nd year (e.g., how it is at UNC), they'll let you skip the first year curriculum, but you'll have to take the 2nd year curriculum and take the qualifying exam the summer after your first year.

You are taking this artificial distinction your school is making between advanced calculus and real analysis too literally.  The advanced calculus courses are what everyone here means you need to take.  It's kind of weird that it is a two semester course though, as usually all those topics are covered in one semester.  You do not have to take the Lebesgue class that your school calls real analysis, but with your profile you will not be competitive without taking the advanced calculus classes.  If possible, I would highly recommend taking them next year because otherwise they will not be on your transcript before applications are due.

I think you're selling yourself really short. First, I wouldn't bother applying to UCSD, TAMU, Rutgers, or Rice. NCSU doesn't have a PhD in biostatistics, although they do have a Biostatistics concentration in their Statistics department. Also, not sure if UW refers to Wisconsin or Washington.
You're competitive for any of the biostats programs in the top-5. In fact, I would be shocked if you didn't at least get into one of UNC or Michigan. I would say apply to all the top-7 biostats programs and maybe those Canadian schools if you're interested. I'd maybe add McGill if you're interested in precision medicine. I'd also add Berkeley if you're interested in causal inference.
It sort of depends. If you've taken all the qualifying exam courses, the department *might* let you take the qualifying exam the summer you arrive. Otherwise, they may force you to retake their versions of the courses and then take the qualifying exam at the end of the first year. It usually depends on both the department and the specific case.
If the qualifying exam is taken in the 2nd year (e.g., how it is at UNC), they'll let you skip the first year curriculum, but you'll have to take the 2nd year curriculum and take the qualifying exam the summer after your first year.

Harvard, Berkley, UW Stats all have at least 3 very top/rising star type people doing causal inference research. An important distinction you have to make is whether you want to do "classical" causal inference  (propensity scores, average treatment effects, instrumental variables, potential outcomes framework) or "modern" causal inference (dags,judea pearl causal discovery,  reinforcement learning, adaptive designs etc...). Both are pretty hot right now but the flavor of research is extremely different.
 

It's a fair question. To me, most of causal inference is concerned with identifying a population average treatment effect (typically not adjusted for covariates), while precision medicine is mostly concerned with which treatment for which individual at what time. Most of traditional causal inference utilizes classical statistical techniques (e.g., regression, GLM, etc.), albeit with some adjustments to account for confounding. In causal inference, it's really important to prove things such as consistency and asymptotic normality.
In precision medicine, a lot of the methods are more machine learning focused. They might prove consistency, but asymptotic normality is a bit rarer.
I guess I just feel precision medicine, while a specific case of causal inference, is a lot different than other fields with specific cases.

If you have the prerequisites, epi and econometrics are good disciplines for causal inference research as well.

If you have the prerequisites, epi and econometrics are good disciplines for causal inference research as well.

UNC is pretty mathematically rigorous relative to its peers, and you will be taking courses alongside first-year PhD students who will have taken (likely) much more math than you. That said, there are many students who have the minimal math background (i.e., Calculus I-III and linear algebra) and are successful. There will be a master's exam that is only required for master's-level students, and if you pass the exam then it's smooth sailing to get the degree.
Also, note that UNC is on a pass/fail system, where the grades received are H (high pass), P (pass), L (low pass) and F (fail). Typically, <10% of students will get an H, almost all the rest of the students will get a P unless they did not do the work or bombed every single test, both of which are rare. I have never heard of anyone receiving an F. You can get two L's and still get the degree, but, again, I have seen very few students get L's.

Yes, this is what most analytics people with jobs do.  There are not a bunch of jobs in this world where people recreate their applied statistics homework assignments and run lack-of-fit tests for their GLMs.  Even most data scientist jobs, at the end of the day, are this.  If you work at a business, your job is "make numbers go up."  Most data science is literally figuring out how to write sql to count things.  I'm telling you as someone who was a data scientist at FAANG, your expectations of the intellectual satisfaction you will get from your job are way too high.  There is not a lot of interesting statistics work to be done because most of it is either: 1) so simple because you have a lot of data (big tech) or well-designed experiments (pharma) or 2) so filled with uncertainty because it doesn't have those things that it's not useful and thus not worth it for a business.  Maybe you'll be happy in an academic lab as a research assistant or something, but industry jobs with interesting statistics stuff are few and far between, and I would not bank on having one of them.

If this is a job opening available, I don't understand why you're not doing it.
I have mentioned data analyst jobs multiple times, which are essentially intro-level jumping pads to data science positions if you don't currently have the skills for that.  From everything you're saying here, it doesn't sound like you would enjoy a PhD very much and I don't think it would help you find a career you like.  You are never going to find a position where you just run linear regressions 8 hours a day.  Even at the best job, most of your time is going to be wrangling data and translating findings (because that's why they are paying you).  If you have an MS in biostatistics, you do not need to go back to school to do what you're looking for.  You need to do some soul-searching and read a lot of job descriptions to think about what you can tolerate doing, and then you need to apply to those jobs or teach yourself some skills so you can expand your options.

I don't agree with this at all. Wake Forest is a very reputable school and there's a list of institutions that their Master's graduates end up attending, many of which are very prestigious. Not sure if you're trying to actually take a knock at Wake Forest in particular or if you were just oblivious to this fact.
I think the OP has a great chance at top-20 programs and a small but nonzero chance at a top-10 stats. I could see them getting into any/all of the top-5 biostats programs. Their mathematics knowledge is extremely deep--far deeper than the vast majority of domestic students. They have a letter writer with connects at the institutions in which they are applying. Got a perfect GRE Q and writing score. This is a really strong profile IMO.
The biggest problem is going to be that it seems the OP has quite specific research interests. I think it will be difficult to find a good program that aligns with these interests.
OP: I recommend you apply broadly (a couple in the top-10, most in the 11-30 range, some in the 30+ range to be "safe"). I do NOT advocate for speaking about your specific research interests in your statement of purpose, because I think if it's not a departmental interest they will be likely to reject you. Simply say you're interested in high dimensional statistics or something.

Parroting @StatsG0d point, I think you're really on the wrong forum. The people in this forum are fundamentally interested in statistical inference and probabilistic modeling. NYU DS (I have researched the department extensively, and even wrote a specific SOP for it and then I realized I wasn't a good fit after I realized how bad the SOP was) and what you seem to be interested in are more in developing computational tools that push the bounds of what is learnable. Rather than being concerned with proving consistency/convergence or statistical estimation problems they're more interested in solving problems like computational tractability, gradient zeroing, algorithmic correctness/efficiency, good representation for efficient information retrieval (See Dynamic Programming Algorithm for Chomsky Normal Form),methods for compressing neural network . Tbh for developing algorithms like EM and MCMC and even impactful NN work which is just optimization, proofs of convergence are extremely important in both fields and ya gotta be good at Analysis.
You should ask around whatever CS/Bioinformatics forums are out there. But to get into programs that attack these problems, you'd need demonstrated competency in CS topics like data-structures, systems programming, analysis of algorithms, numerical analysis. With your research background , which is on the weaker side for CS,  I think you'd need a good theoretical math background. If you're interested in it, I'd encourage you to apply, shoot for the stars man/gal. But if you want to do DL research, Statistics departments are not for you.
 
On a philosophical note that I hope you feel free to ignore as I don't know your entire situation: judging from the thread, it seems like you're seeing a PhD as a silver bullet for the existential pain of working in late capitalism. Unfortunately no matter what you do (yes, even most professors who aren't Michael Jordan or tibirashiani, and definitely most grad students) 80% of your time will be spent doing menial pretty frustrating work, but you have to find the other 20% to make it worth it. And even if the actual job all sucks there's almost always a silver lining in a job if you have  masters (pay which you mentioned, work life balance etc..). If your job is super interesting, it's probably going to have bad work-life balance and the contrapositive is also true. Having a lot of life suck is just unfortunately part of life and being happy is an explicit effort you have to make.
Not to say, you shouldn't try to change, but just having a PhD won't make things better, worse, harder, easier. It won't make you smarter or dumber, it'll just make things different. Seeing things like NYU DS PhD is an attractive solution because it seems so simple, do X get Y. But life doesn't work like that and having a PhD creates a whole host of new problems that you might not be happy dealing with if your primary motivation for a PhD is just that you hate your current job.
For context, I work as a datascientist at a Fortune 100 financial services company, and I hate it so much. Everyday when I wake up I curse Bill Gates for spawning Excel/Powerpoint from the 10th circle of hell. I have to use incredible amounts of MBA jargon, but the second I use the words "conditional on" the MBAs lose their minds. I can say with confidence that my job is probably worse than yours. The job tortured my very soul for a while, until I saw the finale of the office while slacking off from work:
 
I realized that although my entire job sucks, I have the work life balance to spend more time with my family, my aging dog, my girlfriend. I've gotten pretty decent at classical guitar and picked up a bunch of other stupid hobbies (e.g latte art and fishing). I realized that when I'm a graduate student drowning in qualifying exams and research, I'll definitely miss this job that I currently hate.
Sorry, this probably wasn't helpful, but I just want to warn that a PhD shouldn't be viewed as a solution to a problem. It's a luxury and a privileged that you should deeply want.

Even if you get a PhD and get a data science job at Facebook, most of your job is going to be wrangling data and seeing if app downloads went up or down. If you want to do cool statistics stuff, you will have to do it as a hobby or go back to academia.  I understand your dilemma, as this was disappointing to me too, but it's the reality of the job market.  26 isn't old.  If you would enjoy a PhD, you have plenty of time to get one.  But if you're just doing it for job reasons, you may find that the other side is not what you expect, and it would be a shame to do a PhD in that case of you're not enjoying the process.

Yep mostly this (although I do feel like this has been changing in recent years). The top-4 programs are known to be pretty mathematically rigorous. Perhaps not as much as stats departments, but much more than the rest of the bunch.
I think there are some schools that will automatically consider you for MS admissions if you don't make the PhD. You could target those schools. Also, a lot of the programs have a process for internal PhD applications (e.g., I know UNC does). So you could also apply for an MS at a program where you'd like to do a PhD and see how that goes. I feel like that's a better option than applying to MS and then applying to PhD because you'll spend a lot of money in a 2 year MS program.

Biostats programs just tend to have a shallower applicant pool, often with less of a math background.  Outside of the top 5 programs, your math background will stick out more there.
I think top 40 is a little bit of a stretch, but I think schools like FSU might be achievable for a PhD.  Depending on your goals after the PhD, it might be worth to apply to PhD programs now.  I think there are a lot of very good programs in the 40-70 range, but if you want to be a professor at a top department, you may personally find it worth it to get a top MS and reapply if you are willing to spend those extra two years and whatever amount of money.

I had a master's degree from a top-30 stats program, where I took several PhD level courses (Math Stats I-II, Linear Models, Generalized Linear Models). My friend (who is in a stats dept.) from the same school had all those courses + PhD-level measure theory and probability theory, limit theory, and several graduate-level courses in the math department. 
Sadly, we both had more rejections than acceptances.

IMO, what will boost your application the most is none of the above. If you are able to, it's better to take upper-level proof-based math courses, even at the undergrad level. The biggest doubt of your application is your math ability. Consider taking courses like (in no particular order)
Number theory Abstract Algebra Complex analysis

I agree the priority should be real analysis at a legit school.  I do think that PhD stat theory would be very useful though *if* you can do very well AND get a positive letter from the professor who teaches it.  I got a letter from a teacher of my math stats class from my MS degree and I think it helped me.  I'm not sure if the FAANG thing would be worth it over the low-hanging fruit you have to improve your app -- I do think my data science experience was appealing to a lot of programs, but your mileage may vary and I think the easiest thing you can do is take a little more math and work on getting 3 good letters from your current ranked stats program, you're in very good shape for programs ranked 20-50.  The for-profit university thing will stick out, but it's pretty clear you're smart so I don't think it will matter as schools are generally pretty forgiving of things in the past -- I went to a good school for undergrad but failed classes, got terrible grades in early math classes, and pretty much nobody ever mentioned it.

This is a very interesting and atypical profile. First, if you obtained your MS at least 2 years before you will be submitting applications to PhD programs, I highly recommend applying for the NSF GRFP and writing about that in your statement of purpose. Not a deal breaker if you can't do it, but it will tell admissions committees that you're very serious about research and have thought deeply. Based on your background and credentials, I think you would have a good shot.
Now, although you did not do well in undergrad, you have very good grades in graduate level stats courses, which is great. The B+ in multivariable calc might raise a suspicion, but can be overcome by a good grade in analysis. I recommend maybe also taking real analysis II (if you're only applying to stats departments) to show adcoms that your math ability has improved.
I think you definitely have a shot outside the top-20. I think you'll have a better chance in biostatistics programs, which I feel are more likely to admit students with atypical backgrounds / interesting profiles (likely due to the proximity to public health). I feel like with good grades in high level math courses, you have a good shot at biostats programs like UNC, Michigan, Emory, Minnesota, and a really good chance at programs like Pitt, Vanderbilt, etc.
To ease any concerns, hardly anyone has biostats "experience" prior to applying. All the areas you mentioned save for operations research have important and active biostatistics research areas. I'll summarize below, and leave it to you to decide if you're interested in them:
Statistical Learning - Precision/Personalized Medicine Develop / utilizing ML algorithms to find the right treatment at the right time for the right person Typically concerned with proving under some assumptions the resulting treatment rule is optimal High Dimensional Data Analysis - variable selection / genomics High dimensional data arises naturally in biostatistics / public health (e.g., genomic data, electronic health records (EHR) Outlier analysis Can't give a specific example, but outliers occur often in biostatistics (and in pretty much any data application)