Banzailizard

I also did this and got good (and consistent) responses two years ago. I agree with the above that POIs will give you the best feedback, and framing it as "how to improve" is best. As hard as it is, I might also suggest waiting until later to ask-- winter is an especially busy time for most people, and before April 15 people seem either focused on admitted students or done thinking about admissions. At least for me, I was also in a better place to take advice then...I got some pleasant but straightforward feedback that would have felt maybe more personal if it was right after rejections. 
Some other framing devices I used: What does a successful candidate for [field] usually look like? I'm planning on doing x and y to improve, what else can I do to refine my interests? I get the impression that [qualification] is very common in this field, do I need that? I've been working on x, y, z over the summer, do you think it's worth re-applying to this program? 

You could email both, but unless your POI was on the admissions committee, I might advise steering more toward the DGS with such a question.

@Banzailizard Either in your first email or in a follow-up if you get a positive response, you could also ask whether they think the Rutgers MA, specifically, would be useful for any applications you submit in the future. It sounds from your post on this page like you have minimal languages and are applying to a field where you really do need languages, so I would guess the answer is going to be yes, it will be helpful. But if it feels useful for you to have a more specific query, that sounds like an acceptable one.

I am in a similar situation so you are definitely not alone! If you look at my CV from one year ago you might think I'm a Political Science person bc I majored in international politics, took statistics class, and do not have a degree in History .
For my first cycle, I applied to 4 programs in Political Science and 2 in History (Harvard and UPenn), and got  rejected by all of them. After I got the rejections, I contacted my POI (in History), thanked them for taking time to review my application,  asked about how I could improve my application, and if they would recommend me to make an effort and try to reapply for the next cycle. They replied, and it was implied that they've got the impression that my training is half-half, which, among a few other things, played against me. 
I did lots of things in the past year to make sure that i no longer leave the impression that my training is half-half, and that I am a professional with solid research experience in History, by actually acquiring more experience in History and demonstrating this in my SOPs and writing samples. (I did audit graduate seminars in History, though not for the contents of courses but for networking opportunities with more historians who later helped me build a much stronger application for this cycle) 
This cycle I applied to 7 programs, all in History, so far I have heard from 5, and got in 4, all are (in my humble opinion) decent PhD programs. 
Hope this helps.

a few things.
Indeed, frame question is, "I'm interested in strengthen my application for the next cycle.  What might I be able to improve on?" The POI and the DGS will say something.  Your POI, I can almost guarantee you, did read your application and is more likely to remember it than the DGS who has seen a lot more applications that things become kind of blurry.  Both will have application on their computers for reference.  CC on another.  I've done this before and it worked out just fine. They will usually stress the statement of purpose, language training or experience.  GPA and GRE, they know, just need to be above minimum Graduate School (3.0 GPA and I don't know the GRE these days) and those hard to raise.  I highly doubt that they will want to see "credits" for language training; you can simply show your proficiency through your writing sample. 
What I have learned is-- don't ask just one school, ask a few to find a bit of common pattern.  I do want to believe that many will try to be honest with you.

Saw this checked my status with Minnesota but no change for me.  Still says "awaiting program decision." Wonder what that means for me. I am assuming it's a rejection on my part.  Hope that means you are getting in though since it was your top (and only) pick.

There are too many variables for one p-value to determine causality.  I was a poli-sci minor, so I had to take quantitative research methods. I did a paper on the application of Hofestede's Masculinity Index on the election of women in worldwide parliaments. I hypothesized that more masculine societies voted for more women (opposites attract hypothesis). This ended up being founded.  More masculine societies were more likely to elect WOMEN. However, it was not because they were more masculine societies, even though that's what the p-value suggested.  There are many other factors, the largest being a UN sanction that bars certain nations from receiving funds through the IMF unless their parliaments are representational of the gender distribution of the population. There is a religious factor- Muslim countries (score high on the HMI) are more likely to elect women. More educated societies are more likely to elect women (High HMI). Countries at war are more likely to elect women (High HMI).My p-value (<.001) was good, but the hypothesis was not. 
Correlation does not equal causation. P-value can null a hypothesis, but it cannot prove a hypothesis true.

It is likewise better to critique economic work with an understanding of economic theory and methodologies rather than systematically denouncing it because you don't understand it.
The purpose of Nations isn't to establish a history of international economic development - that would be impossible. It is a pop science monograph based on Acemoglu's work on institutions and development, which largely uses contemporary datasets and is built upon a strong foundation of institutionalist work by other economists. I'm surprised that the notion that institutions aid economic development is controversial to you; it's pretty much an accepted axiom with a lot of theoretical and empirical backing in economics at this point. Perhaps Acemoglu can be tasked with misusing a historical metaphor, but that's not really relevant to the science behind the claims. Economists could improve on the outreach and communications front, for sure, but to claim that one of the most prominent practitioners should be "denounced" based on his literary journalism is ridiculous.
As for your critique of p-value, yes, ditto, and this is not a mistake economists make. A p-value doesn't determine a regression's validity - and it certainly has nothing whatsoever to do with causality. The misinterpretation of p-values is a prominent issue, but in fields that do not have an institutional legacy of statistical methods, such as, I'd imagine, history. Statics absolutely are a valid method for making "scientific" conclusions - if they are applied correctly.
The closest thing to economic history produced by economists that I know of tends to be essentially an exercise in long-run statistical inference. It's an interesting exercise and has applications in other economic work, but it is understandably far from the concerns of historians. In my layman understanding of history, historians ask different questions about past events than economists, answer them in different ways, and are looking to arrive at different results. It's not obvious to me how statistical work outside of descriptive statistics could be integrated at all into historical scholarship or what the benefits of doing so would be. That doesn't mean historical work is bad. That doesn't mean it needs to be "ripped apart". Before you rip apart a piece of scholarship, especially outside of your purview, consider whether the question you're interested in is the question it's answering. Both economics and history have valuable insights about society, as do anthropology, political science, literature, and visual art, and those insights may be very different, which is their strength, and we don't need to have a dick-measuring contest about which are more valid. 

Allow me to take a step a bit further.... negotiations are best done when you have more than one offer in hand and your favorite program's package isn't as good as the best funding package you've got.  Otherwise it's hard to justify why you need more money to come... and, oh, don't declare "thank you for your acceptance!  this is my TOP choice!" until you've heard from other schools.  Not saying so upfront will help your case a bit when you have another offer and can negotiate. You need plenty of carrots to eat, not just one.  (I spoke a little too soon declaring my current program a top choice but my adviser had said that the funding was still being negotiated with the Graduate School so I used the opportunity to mention a very prestigious fellowship that I was being offered by another program. After all, she wouldn't want me to come knowing that I might have given up a better package  )

I would say it is fine to mention that a school is your top choice if that is true, but I would not suggest you would commit if admitted.  The former might be held in your favor if debating between two equally qualified candidates.  There is even a post about it in the stickied retrospective thread at the top of this subforum.  However committing to attending would be less advisable because it gives you less room when negotiating funding.  Yes its not a legally binding contract, like say, early admission in undergraduate, but saying you would commit is a promise and breaking it (or suggesting you will break it to negotiate) is just a good way to burn bridges early in an academic career.
I would wait for a second opinion because I am not sure how valuable my advice is.
All my apps were due December 1st.  Good luck to everyone who has them due today.  Take a short break before you hit submit and come back to review the materials with a fresh mind.

So how is everyone else doing?
I hit a stumbling block earlier but, thanks in large part to this thread, I am more or less back on track. I very specifically started this season with some deadlines which I have mostly met. August was for background reading and looking at bibliographies to see where to search. By September 30th wanted my schools identified (in retrospect I wonder if there is an optimal stopping method for this).  By October 31st I wanted all my SOP done: bit behind here, took an extra week, but now they are semi-finalized. Content is set, now just small tweaks. I sent them out again for reviews.   Took a break on a day that I was out of it to do the mindless work of filling in the applications. All done there, other than the stuff that counts. LOR requests are out, 7/12 are submitted. November is for my WS revision. To catch back up I temporarily suspended working on foreign languages. 
So overall, starting to feel the stress of the irrevocable deadline, but keeping it together because the arbitrary (i.e. unweighted with the actual effort or importance of any given task) progress bar I made looks pretty full.

Keep in mind, professors do recognize that interests change.  The point of the WS is to demonstrate your skills thus far as a historian-- how you integrate and analyze contemporary historical debates on the questions you're asking and how you use primary and secondary sources to support your argument.  Your SoP will be the spokes-item of your present research interest and that's wha the profesosrs will judge on when determining your fit to the program. Make sure that your SoP clearly articulates how you moved from that topic of  your WS to your present interest.  Share these concerns with your letter writers and they'll be able to frame your application pacage better (they have far more leeway in space than you do).

Without knowing more about your writing sample, the following guidance is spit balling.
Shift the focus of the paper so that it centers around the contemporaneous debate(s)/initial historiography in English.
Beginning Event A happened in 18xx in Egypt. Summary of historiography. Pivot to earliest discussion of Event A in English and how that discussion shaped subsequent views. Summarize why understanding earliest discussion is important. Middle Primary source-based discussion of Event A (it sounds like you have this already.) Primary source-based discussion of initial interpreters of Event A (letters and papers of English-language interpreters) In depth discussion of influence of initial interpretation over time. Some secondary works are now primary sources End Tie in your piece with broader conversations of the lasting influence of initial interpretations upon historiography and history.  Historiography as knowledge, knowledge as power. You can go big here. 30K, 60K 100K views. Avoid jargon. Avoid getting too wrapped up in various theories unless you really know the theories and you believe in those theories enough to not get an offer. A disinterested Joe Friday "just the facts" approach will do. If possible, make an elegant pivot to your current research interests. A cluster of well phrased questions. Speculation on how you would use your new interests to address the broadest of the questions. The linkage between this revised piece and your SOP should be clear to anyone who reads both. #HTH.

I went back to around page 5 looking at threads and this seems closest to what I am looking for, which is some general advice.  If this is the wrong place I am sorry. This is my second time applying for PhDs but first for history. 
As background I graduated in 2013 from a small-ish state school (6k students in total) with a double major in History and Economics.  GPA was 3.5 with a 3.7 in my history major.  I took the GRE's and got 169 Verbal  162 Quantitative 4.5 Analytical writing.
I have been working full time since graduation to pay off student loans.  Last fall I started applying to PhD programs in economics, with a particular interest in economic history and ultimately working in academia.  I was not accepted to any of the PhD Programs. I was told my quantitative score was far too low. I also definitely applied too late and rushed the application process.  I was accepted for an unfunded masters which could progress into a funded PhD. I (quite literally) calculated I could not afford the debt of unsubsidized student loans and politely declined.
I had a nice call with my econ advisor, and she asked why I had not also looked into history.  Truthfully, I figured Econ, with its heavy mathematics and public policy connections, would hedged my bets better for a fall back to non-academic work (think-tanks, finance, and tech firms) since the academic market is questionable. I reached out to a history professor I took a number of classes with, and who works in economic history.  History might be a better fit based on my interests.
His general advice was 1. Find a good mentor, meteors can make or break you. He suggested reading books by people I was interested in working with. 2. Assuming I get to graduate school, publish like crazy. He had 26 papers published by the time he defended his dissertation. Admittedly easier said then done; his mentor gave him a big boost by co-publishing with him at first to get his foot in the door.
That was in May, so I have been looking through programs, starting with higher ranking ones, specifically at faculty, and have been reading books of the people I might be interested in working with.  I have only really started getting into this research seriously though, with a shift from more-then-full-time to part-time work.  I do have some problems:
1. I know the emphasis placed on good LOR.  I was closer to the econ faculty at my school and had 3 LOR from them for the econ applications. My history professor offered a LOR, I might have one other I could ask for a LOR but I only had one class with him.  I am not sure if it is better to ask two of my econ professors again and then have my history professor be my third or try to get a letter from a history professor who does not know me as well.
2. My undergrad classes were unfocused, and related, I am still narrowing my topic down.  This is a list of what I took:
Early Russia (Kievan Rus), Byzantine History, Empire and Democracy in Athens (Peloponnese War), History of the Czech Republic (while abroad), Framing Pre-modern World History (seminar on how to teach pre-modern history, historiographic in nature), Early Imperial China (ending at the Song dynasty).  In addition I was required to take two general world history courses (pre-modern and modern) and a historiography course.  For my economics degree I was required to take a intellectual history course in economics.
I did my thesis in history on the Egypt under the Muhammad Ali Dynasty, specifically about their westernization and entrance into the world markets, and in econ I did a economic history paper on the effect of British hegemony on global trade in the 19th century by trying to draw conclusions using a linear regression model.  It was not a great paper, but got me used to working with historical statistical problems (mostly that historical statistics are hard to find and have lots of holes).
As for a topic I am trying to narrow down but in general my interests fall in the late Medieval, Early Modern, Early Industrial Era in Europe, and in particular economic and quantitative history (maybe eventually complexity theory), demographics, labor history, and the development of early capitalism and global trade.
3. In terms of languages other than English I have one: German and I have not done any primary source work in it.
Other than these problems I have some general questions:
1. How narrow does my focus have to be in terms of time, place, and topic?  My inclination is to as broad as possible, but I understand that is not how academia works, so its a balancing act.
2. Assuming I can narrow my topic down and put together a strong SOP, should I be applying for the 2018 term? Would an attempt at a funded MA be better to focus my research?
3. Assuming yes to either of these, are there individuals or programs outside of the LSE which have a strong economic and quantitative history offering, or would be supportive of quantitative and interdisciplinary approaches to supplement more traditional sources?  I have found, so far, only Michigan which offers an "Economic / Societal History, Quantitative Methods" focus, and maybe some of the faculty at Berkley, Northwestern, and MIT. I might be looking for the wrong terms though.
4. Does anyone has a reading list in these topics? I have some background from all the world history I took, but I am trying to read as much as I can to get a feel for what questions have been answered and how.

I went back to around page 5 looking at threads and this seems closest to what I am looking for, which is some general advice.  If this is the wrong place I am sorry. This is my second time applying for PhDs but first for history. 
As background I graduated in 2013 from a small-ish state school (6k students in total) with a double major in History and Economics.  GPA was 3.5 with a 3.7 in my history major.  I took the GRE's and got 169 Verbal  162 Quantitative 4.5 Analytical writing.
I have been working full time since graduation to pay off student loans.  Last fall I started applying to PhD programs in economics, with a particular interest in economic history and ultimately working in academia.  I was not accepted to any of the PhD Programs. I was told my quantitative score was far too low. I also definitely applied too late and rushed the application process.  I was accepted for an unfunded masters which could progress into a funded PhD. I (quite literally) calculated I could not afford the debt of unsubsidized student loans and politely declined.
I had a nice call with my econ advisor, and she asked why I had not also looked into history.  Truthfully, I figured Econ, with its heavy mathematics and public policy connections, would hedged my bets better for a fall back to non-academic work (think-tanks, finance, and tech firms) since the academic market is questionable. I reached out to a history professor I took a number of classes with, and who works in economic history.  History might be a better fit based on my interests.
His general advice was 1. Find a good mentor, meteors can make or break you. He suggested reading books by people I was interested in working with. 2. Assuming I get to graduate school, publish like crazy. He had 26 papers published by the time he defended his dissertation. Admittedly easier said then done; his mentor gave him a big boost by co-publishing with him at first to get his foot in the door.
That was in May, so I have been looking through programs, starting with higher ranking ones, specifically at faculty, and have been reading books of the people I might be interested in working with.  I have only really started getting into this research seriously though, with a shift from more-then-full-time to part-time work.  I do have some problems:
1. I know the emphasis placed on good LOR.  I was closer to the econ faculty at my school and had 3 LOR from them for the econ applications. My history professor offered a LOR, I might have one other I could ask for a LOR but I only had one class with him.  I am not sure if it is better to ask two of my econ professors again and then have my history professor be my third or try to get a letter from a history professor who does not know me as well.
2. My undergrad classes were unfocused, and related, I am still narrowing my topic down.  This is a list of what I took:
Early Russia (Kievan Rus), Byzantine History, Empire and Democracy in Athens (Peloponnese War), History of the Czech Republic (while abroad), Framing Pre-modern World History (seminar on how to teach pre-modern history, historiographic in nature), Early Imperial China (ending at the Song dynasty).  In addition I was required to take two general world history courses (pre-modern and modern) and a historiography course.  For my economics degree I was required to take a intellectual history course in economics.
I did my thesis in history on the Egypt under the Muhammad Ali Dynasty, specifically about their westernization and entrance into the world markets, and in econ I did a economic history paper on the effect of British hegemony on global trade in the 19th century by trying to draw conclusions using a linear regression model.  It was not a great paper, but got me used to working with historical statistical problems (mostly that historical statistics are hard to find and have lots of holes).
As for a topic I am trying to narrow down but in general my interests fall in the late Medieval, Early Modern, Early Industrial Era in Europe, and in particular economic and quantitative history (maybe eventually complexity theory), demographics, labor history, and the development of early capitalism and global trade.
3. In terms of languages other than English I have one: German and I have not done any primary source work in it.
Other than these problems I have some general questions:
1. How narrow does my focus have to be in terms of time, place, and topic?  My inclination is to as broad as possible, but I understand that is not how academia works, so its a balancing act.
2. Assuming I can narrow my topic down and put together a strong SOP, should I be applying for the 2018 term? Would an attempt at a funded MA be better to focus my research?
3. Assuming yes to either of these, are there individuals or programs outside of the LSE which have a strong economic and quantitative history offering, or would be supportive of quantitative and interdisciplinary approaches to supplement more traditional sources?  I have found, so far, only Michigan which offers an "Economic / Societal History, Quantitative Methods" focus, and maybe some of the faculty at Berkley, Northwestern, and MIT. I might be looking for the wrong terms though.
4. Does anyone has a reading list in these topics? I have some background from all the world history I took, but I am trying to read as much as I can to get a feel for what questions have been answered and how.