insert_name_here

People leave their PhD programs with an MS all the time.  I would be utterly shocked if your program did not allow this.  Talk to your advisor/the grad program chair and figure out how you can stay and leave with an MS.  Your first year of courses is probably the same, so even in the worst case that they cut off your assistantship, you'd still save money compared to starting over somewhere else.
You can re-apply and I'm sure you'll have a lot of success, but really ask if that's the best path for you.  I'd do anything I can to try to make it work at your current program to leave with an MS, which will save you lots of time and money.  And you go to a top program, so it doesn't make sense to transfer down.

Not even close, these programs are not in the same tier.  UW

I think the Berkeley masters program is great, but it is worth noting that the following sentence is written in bold at the top of the program's homepage: "The focus is on tackling statistical challenges encountered by industry rather than preparing for a PhD." 
Unless you've had specific assurances beforehand, it would seem ambitious to plan on doing research in such a program. I don't know Stanford's program as well, but in general it's best to assume that being a masters student in a department won't help you get in as a PhD student, and that you'll have a hard time finding meaningful research work. (I would expect, but can't verify, that neither of those departments has had a single masters student move onto their stats PhD program in the past 5 years).

I think the Berkeley masters program is great, but it is worth noting that the following sentence is written in bold at the top of the program's homepage: "The focus is on tackling statistical challenges encountered by industry rather than preparing for a PhD." 
Unless you've had specific assurances beforehand, it would seem ambitious to plan on doing research in such a program. I don't know Stanford's program as well, but in general it's best to assume that being a masters student in a department won't help you get in as a PhD student, and that you'll have a hard time finding meaningful research work. (I would expect, but can't verify, that neither of those departments has had a single masters student move onto their stats PhD program in the past 5 years).

Not so sure why people think stanford is better than berkeley.  It is a smaller department than berkeley.  It is mostly theoretical.  Berkeley has much closer ties to EECS and does a lot more applied and methodological research Not getting into the politics of this however A lot of people have complained about the lack of diversity at stanford.  I have heard many female applicants accepted at Stanford have rejected it because of its diversity reputation.   I am not sure if they have ever had a black or Hispanic phd student at stanford.   

Your list looks pretty reasonable, I'd expect you to get into at least half on your "others" list. I'd add a couple more higher ranked schools that may fit your academic/personal interests (CMU? UW? Berkeley?)... I wouldn't say you're super likely to get into those places, but definitely not a waste of money.

How sure are you of those research interests and how passionate about them are you?  Some people can be truly fulfilled by their research and if that'll make you happy, go to Berkeley.  But you're not even going to be able to do good research if you're unhappy and wishing you were on the other side of the country.  Are you sure that you are that much interested in probability than say, MCMC, where you could work with Xiao Li Meng at Harvard who to me is one of the most interesting people in statistics - just read some of his paper titles and listen to his talks.  Are you sure that theoretical machine learning at Berkeley is that much more interesting to you than the reinforcement learning that Susan Murphy is doing?  There's plenty of theoretical stuff going on at Harvard that might satisfy you intellectually, and I definitely think that location is extremely important.  The facts are that you will be qualified for top stats jobs after working with someone good at Harvard.  Maybe Berkeley will offer you a slightly better chance at doing the type of ML that gets a FB research job, but is that extra slight chance worth 5 years?
My recommendation would be to download some papers from profs you like at both school.  Read the papers from Berkeley and ask yourself if you love reading about that subject so much that you would move across the country to Berkeley to be able to ask the person who wrote it a couple questions every week.

Here's a hot take on how I think academic institutions SHOULD operate in an IDEAL world. 

1) Admit any one who wants to attend based on a college entrance exam (kind of how its done in some foreign countries)
2) In specified periodic time intervals, there are qualifying exams to be taken. Those that fail below a certain cutoff will have to leave the school (analogous to PhD exams) 
3) Those that can finish all the coursework and pass all the exams are able to graduate (schools graduate too few/too many students a year should be audited for quality of education)
This is not to say problems with AA and gender bias would disappear, as those with the privilege of accessing resources from a younger age would still benefit - they always will. But this way opens up a larger playing field, where everyone has a chance to succeed, and whether a student can study at an institution is not dictated by a biased admissions committee who decide your capability to succeed based off of a few pieces of paper.
And this way, instead of diversity becomes a moot point, and they would admit you based on your capabilities that you will prove yourself rather.

This is just my hot take, please don't downvote me into oblivion. I understand that there resource constraints that render all of these steps infeasible. But something just doesn't sit right with me in the current way admissions in grad and undergrad are handled. 

Saw this virtual panel apparently from UC-Berkeley and Michigan Stat PhD students to answer questions about Stat PhD admissions and whatnot, and figured people who come here might also be interested in it.  I claim no knowledge of these folks, but Rob Santos tweeted this out, so I'll take the liberty of assuming he hasn't gotten hacked or whatnot (and I haven't seen anyone else post it; if they have, we can delete this).
Anyways, the panel is at 7 PM Eastern time on Oct 13 (today/tomorrow, depending on how you delineate that).  Here's the link:  https://www.statsphd.com/ to their site, or the Zoom registration directly to save you a click:  https://umich.zoom.us/webinar/register/WN_R9Bjv3IdRoqmrdygdnkNPA 

I've never heard of anyone caring about a Ph.D's GPA, in any setting. I have a Ph.D, and honestly don't even know what my GPA was.

If all three are from quantitative professors, get the one that will be the most positive and have the most to say.  I would guess that's probably 1.  If you have some poor math grades, maybe the real analysis prof will help, but if your math grades are good I'd probably go with 1.

Calling Berkeley/CMU particularly mathematical is a bit of a reach. While they can both be mathematical if you want, you can also graduate from Berkeley without taking a single probability/measure theory class. CMU also requires all students to do a faculty-supervised data analysis project over two semesters... not many departments have that. Fully agreed on Stanford though - to them, if there isn't a mathematical proof, it isn't statistics

Calling Berkeley/CMU particularly mathematical is a bit of a reach. While they can both be mathematical if you want, you can also graduate from Berkeley without taking a single probability/measure theory class. CMU also requires all students to do a faculty-supervised data analysis project over two semesters... not many departments have that. Fully agreed on Stanford though - to them, if there isn't a mathematical proof, it isn't statistics

There are *many* faculty in Statistics/Biostatistics departments conducting research and publishing in the top journals and the top ML conferences in the areas you mentioned (high-dimensional statistics, causal inference, etc.). Most students are capable of self-teaching themselves these topics (or taking electives to gain some exposure to them) after they begin their research.  I think it is somewhat unreasonable to expect programs to teach students all they need to know for their research through courses (when a PhD is largely about teaching yourself and contributing new research that isn't already covered in classes) or to tailor coursework around what's "trendy" at the moment. For one, not all students are interested in the same things. Classes on optimization likely have little relevance to students who are interested in applied probability/stochastic processes, for example. Nevertheless, as I also mentioned above, most Stat and Biostat programs are taking it upon themselves to 'update' the curriculum to also include the more current topics. 
Secondly, the other fields you mentioned might have a lot of coursework too that isn't directly applicable to students' research. For example, in an Applied Math PhD, students might need to take two semesters of graduate-level Analysis with measure theory, Hilbert spaces, functional analysis, etc., as well as a lot of classes like numerical analysis, partial differential equations, etc. These students typically also need to pass several written qualifying exams. An EECS student might need to take classes on computer architecture, theoretical analysis of algorithms, etc. But if these Applied Math or EECS students then go on to conduct research in machine learning or global optimization, then it's not like all of their classes are immediately relevant to their research.
Now, some of the top programs in these other fields (like Stanford CS, Princeton Applied Math, Berkeley EECS) likely do keep the coursework requirements to a minimum (so most students are largely done with classes by the end of their first year, and students also have greater flexibility in what classes to choose -- so they probably do only take a few classes that are immediately relevant to their research). But that's mainly because the types of students that are admitted to these kinds of programs have already completed extensive graduate-level coursework as an undergrad and have already done research as an undergrad that got published in major journals or conferences. But these are exceptions rather than a general rule. Most PhD programs in Applied Math, EECS, and IE have at least two years of coursework, and certainly, not all of it is relevant to every student's research.  

Also sorry OP that this thread has gotten distracted - I did an applied stats PhD at a top school, and got some exposure to admissions, feel free to DM me if you have any other Qs.

Isn't that more due to the fact that MIT primarily only has people in either ML or high-dimensional statistics (and in this case I feel like the opportunity of working with Candes at Stanford or Wainwright at Berkeley is probably better than being at MIT), but there's more to statistics than these two fields: what if the person wanted to do something in causal inference or post-selective inference? MIT would clearly be not as great compared to other top stats programs. Additionally what makes a good EECS application is pretty different from what makes a good stats application: applying to EECS in ML usually revolves around having published somewhere in ICML or NeurIPS (sometimes even multiple times) as an undergrad, and comparatively grades/coursework really don't matter that much. 
 
Perhaps this is true in general about stats program curricula being outdated but if we are comparing Stanford/Berkeley to MIT this isn't really that true nowadays. People in the stat department who are interested in ML are encouraged to go take courses in optimization and information theory (which is what I am doing) because as you said, they are very useful. In fact one of the core courses at Berkeley gives a brief introduction to information theory because of how useful it is. But again, not everybody wants to do ML/data science/what-ever gets hyped up in the media nowadays and places like MIT EECS/Math or Princeton ORFE are really niche recommendations since they tend to lean very heavily towards a small subset of areas within statistics and have virtually no presence elsewhere. Also about your point for professorship, I know Berkeley gave out 3 offers for faculty last year, and 2 of them are for somebody with a traditional statistics background.
@kimmy sorry for the sidetracking but the people on this forum are pretty good at giving advice on applying to stats programs (probably because there are a few stats professors running around on these forums). I'd be somewhat more skeptical of any advice you'd receive here about applying to math or EECS (as to the best of my knowledge) because there aren't any similar such people on this forum and you should probably go look elsewhere for advice but do consider these options if that is something you are interested about. 

Lol so uhhhh this guy just spam downvoted all my recent posts again? 
If you agree this is childish, can you just stop it?
Or maybe some mods can do something...
I sincerely have no interest in this sideshow.

Also sorry OP that this thread has gotten distracted - I did an applied stats PhD at a top school, and got some exposure to admissions, feel free to DM me if you have any other Qs.

Lol so uhhhh this guy just spam downvoted all my recent posts again? 
If you agree this is childish, can you just stop it?
Or maybe some mods can do something...
I sincerely have no interest in this sideshow.

I'm sorry, I just can't let this stand unchallenged. It is complete nonsense to say that GLMs have had little impact on data science. Talk to any practicing data scientist and they'll tell you that a lot of the models actually being used in practice are relatively simple regression models. And survey sampling? That's a special case of weighting, which is heavily used in machine learning in the case of rare events (and also to increase algorithmic fairness). 
If all you're interested in doing is creating algorithms that do something faster or more accurately, sure, maybe you don't need a ton of statistical training. But, if that's all you're interested in doing, you're not really interested in being a statistician! Statisticians seek to develop tools for better data analysis, which includes quantifying uncertainty, carrying out inference, and improving model interpretability. It's impossible to do that without a solid grounding in the kind of old-fashioned statistics you look down your nose at.
Lastly, your conclusion that it is better to attend EECS/ORFE programs like MIT/Princeton because graduates from these programs have obtained positions in top stat departments is flawed. Top departments are often looking to find the smartest people they can hire, on the logic that they'd rather have a rock star who does something a little bit outside the norm than an "excellent-but-not-exceptional" faculty member who fits easily within the field. Sometimes, those brilliant people are in non-stat programs, but they're being hired because of their brains not because of their training. Indeed, if they were equally brilliant but had been trained in a stat department, they might be even more attractive candidates! Most people in EECS/ORFE programs will end up in those disciplines; entering such a program with the goal of entering a different field upon graduating is taking a huge gamble that you'll be so exceptional that hiring committees will overlook the fact that your research and training is unorthodox.
OK, rant over.

All domestic students can get in state tuition after one year, so I doubt saving one year in state (~$10k) matters too much.

Unless you had a whole bunch of deep conversations with the COPSS winner, go with the hospital person you did research with for your letter.
I'd add a school or two to your list, but it looks reasonable (Maybe a "dream" school, and one or two lower ones). You've got great grades from a great school, don't stress.

The main purpose of letters is to demonstrate your research potential. So, it's a good idea to get letters from people you did research with. If you co-authored something with them, surely you spent time with the hospital prof, or one of their students/postdocs. Particularly given you have no other research letters.

If top 5 means Waterloo/Toronto/McGill/maybe UBC, it's worth throwing in an application to Berkeley/Stanford. FWIW, Berkeley has accepted otherwise remarkable students without real analysis, though it is rare. Columbia is less competitive than CMU/UW, they'd be worth a shot regardless your undergrad school. 
 

I'll just add - if I were OP, I'd ignore most of what's being said in these past couple of posts. There's certainly some truth to it, but also some reaches... I'm not going to engage beyond that.