zling

If you're applying to the US only to get a job, I think you should take a careful look at the statistics. The H1B visa quota is about 80,000 per year, and in 2017 there were around 235,000 applicants - that means, only around 1 in 3 were able to work in the US. (https://redbus2us.com/h1b-visa-2017/) [This is something I am also considering as an international.]
Will you be happy spending $70-80k in total for a CIPA degree, with a 60% chance of being denied a visa and having to return home? If the answer is yes, then it may still be worthwhile for you. If the answer is no (as it seems from your posts above), then you shouldn't put yourself in debt for it.
Have you tried looking at Canada or European schools and/or jobs, since you said you don't mind working in those countries? I'm not familiar with their system, but at least there won't be the uncertainty about whether the H1B quotas will be tightened. Good luck!

@Revolutionary
Policy is not a specialization. That's like saying you want to specialize in engineering. As regards interdisciplinarity, sure, most policy people have an interdisciplinary skillset - but that is not the same as having an interdisciplinary focus. Until you grow to the heights of Jim Kim or Noam Chomsky and can permit yourself to pontificate on whatever you damn well please, regardless of what they call you doctor for, you need to have a niche in order to get work. A narrow one. A niche in policy is something like innovation policy, or productivity analysis, or aquaculture in west africa. 
I know some people who went the MPA - PhD route to stay in the country (which is unfortunately a necessary reality when you graduate from a middling MPA program and have no work authorization), among a broader circle of people who do so with whatever degree. None of them are at good programs, and none of them are getting academic jobs. Barring a strong undergraduate record (at a known university) or extensive work experience, the MPA isn't really a good gateway to a PhD. It maybe qualifies you for average polisci programs, random interdisciplinary programs, and public policy PhDs (for which academic jobs statistically do not exist). If you go that route, you need to realize that all you're doing is buying yourself more time to find a job.
I can put you out of your misery: this field does not exist. Name any policy area, and you can spit and hit 10 specialists that have 3 citizenships, 5 languages, and star-studded resumes. If you want to work in an in-demand field, you're barking up the wrong tree. Try IT or finance. Nobody works here for the easy career progression or the piles of money; we do it either because we love it, or because we fell into it. What you can do to become an in-demand person is to 1) have a niche you are expert in (because you love it, because you're good at it, because you fell into it and stuck with it); 2) have a skill you do really well (statistics, writing, negotiation, etc); 3) be easy to work with (attitude, attention to detail, organization, good under pressure). 
That said, I agree with the other dude. If this is an itch you need to scratch, go for it. I'm more or less convinced that your discontent can be explained by a combination of growing pains and a lack of experience with having real problems, and I personally give you low odds for success, but then I'd give anyone in your position, broadly, low odds for success and yet some people make it. Just do a conservative cost-benefit analysis before you go.
I know nothing about Fulbright. Cap-exempt organizations are universities and NGOs associated with universities. As for your plan for getting a PhD and "settling" for an academic career, it makes you look completely clueless. The takeaway I want you to get from this post, if not this conversation overall, is that, if you are in the US on a visa, you ALWAYS have to plan for the possibility that you will be going home, because as long as you are on a visa, that possibility is always there. The second takeaway is that, so far, the ideas you have for keeping that eventuality at bay are either unrealistic or have very low odds of success.

1. The idea that you can get into a PhD program simply because you did an MA at Cornell is misguided.
2. The idea that you should do a PhD as some kind of last resort is incredibly misguided. A PhD is a multi-year commitment that's hard to get through even if you come in with all the passion in the world. 
3. The idea that you would then get a job at a North American University with your PhD that you aren't really passionate about and in a field you didn't actually want to be at is just plain offensive. The academic job market is ridiculously competitive. Those "lesser tier" jobs you're describing will still be highly competitive. The idea that you can go into academia as some kind of backup is just so incredibly misguided. More likely, you'll be miserable and depressed doing something you don't want to do, leading to poor performance, and therefore to failure to get a job (or graduate). Sorry to be harsh, but you have no experience and no actual academic interests. You'll be competing against people who actually want to be where they are. It's tough enough even when you have everything going for you, and almost impossible otherwise. If this is your backup strategy, I highly recommend that you go back to the drawing board. 

Is there a way for you to delay graduating -- e.g. take a leave of absence to recover, restore your mental health to a better place, diagnose and treat your ADHD, and catch up on work? It's too bad someone didn't suggest this for your spring semester (and frankly, even for the fall semester) and it might be too late now, but if possible, I think the thing to do is to talk to your advisor and/or your DGS both about the ADHD and about the grieving process, and see if you can make up some lost time and stability by slowing down. You say that you work hard and don't take breaks -- that too isn't healthy, and isn't actually a good way to catch up or keep all your balls in the air. It's pretty much a guaranteed way to wear yourself out and eventually drop balls all over the place. So given that you were on the right track last year before your father died, you can't quite rewind to that point, but you could ask to be given a chance to put the pieces of your life back together and try again when you're freer to concentrate on your studies. I don't know how this would work technically, there may be financial difficulties (and visa issues, if you're international), so this would be something to discuss with the DGS sooner rather than later. But overall I think the situation is such that your professors can't judge your abilities fairly because your work has suffered from external circumstances outside of your control, so the best argument you can make is that you are still passionate about a PhD and you'd like the chance to earn their good opinion and support, once you've had time to process what has happened in your life this year and recover. If you have extra time to concentrate on your work once you've dealt with other issues, I hope you'd be able to get to a place where your advisors would be happy to support your PhD application. 

What did you end up choosing?

I felt that these are complete opposite programs:
- quarterly (Chicago) vs. semester (Georgetown); 11 electives at Chicago vs more requirements at Georgetown (thesis/capstone and only 18 credits left for electives)
- Chicago is more research center focused. Georgetown's research centers were an afterthought in their presentation to us. You will also learn from researchers vs practitioners.
- local/municipal policy vs DC/federal
- Harris expects cohort size to be twice the size of McCourt - expect class sizes to be different
UChicago is known to have a distinctive teaching/learning style. I recommend you read up on that. The type of quant you learn in each program is different. I recommend you look at syllabi and compare/contrast.
It's choice of personal fit, ultimately. I will second @3dender: think about what you want to do after the program. You have to think like an MBA student and do some career planning. At least for me, I saw a clear difference in each admitted student FB groups (join them if you are not in them already).

@zling My other schools should be in my signature.  My main factors in applying were the quality and location of the programs.  I'm different from most applicants in that I'm older and with a family, so it had to be some place we would all like to relocate for a couple of years (my wife's skills are easily transferrable).  We currently live in a small town so were excited at the idea of moving to a major city for a couple-few years.
I'm in it for more of a generalist degree than you are -- as I mentioned above, I see myself working in the non-profit sector doing policy research and advocacy.  I also wasn't sure about the strength of my candidacy after such a long layoff and "merely" being a public school teacher for the last decade or so.  So I applied to the major programs -- Berkeley, Chicago, Duke, Columbia -- as sort of a prayer, while being sure to line up some back-ups behind the next tier (I had a list of 3-4 that didn't have apps due until April, just in case I didn't get in anywhere).
Happily, it turns out I could have applied to way fewer schools.  American was my first acceptance and made an extremely attractive offer along with a terrific recruitment event for their "top prospects" -- they're clearly trying to move up in the rankings and compete with GT and GW as best of DC.  I've kept in touch with a couple candidates I met there who both told me that despite getting into way better programs, they haven't liked any of them as much as American when visiting.
After that, it was basically going to come down to who gave me the best offer.  Chicago, even though much more expensive, was enticing just for its name, until I visited of course.  LBJ didn't offer money but was still the cheapest out of any of them -- alas, in the interim my wife and I decided that Austin was a little too similar to the Raleigh-Durham area that we currently live in.  Berkeley, Columbia and GW didn't offer me money and declined to negotiate, making the decision on them easy.   Duke came in with a generous offer, basically a half-ride, which was less than American, but difference in living costs made it still way cheaper.  And finally I got offered a full-ride from Maryland.
So it was pretty easy to whittle the acceptances down to American, Duke, and Maryland.  Duke is the least appealing location for us, since we already live here, but there's an obvious convenience factor in not having to move with two young children, find schools for them, get a house, etc., all while starting grad school and my wife at a new job.  When you combine that with the significant difference in prestige between Duke's degree and the other two programs, it's really kind of a no-brainer.  As i write I'm waiting to attend Duke's Open House tomorrow, just to make sure I don't have the same sort of visceral reaction I had to Harris.  Assuming I don't, I'll be able to commit shortly (still trying to get them to up their offer after Maryland's full ride!).  Because my wife and I still want to move at some point, we've compromised and committed to relocating after I graduate in two years.
That was maybe more in depth than you were expecting, but what can I say? Like many, I enjoy talking about myself.  I'm not sure how helpful that will be for your own decision, but as a more "mature" applicant I will offer you some unsolicited advice: think long and hard about what you see yourself doing in two years after you graduate, then in five years, then in ten years.  If you're set on IR, there are logistical factors like geographical location that make DC more convenient.  But being, presumably, less attached than me in other areas of your life, you also don't have to follow the path of least resistance.  Ask yourself which city appeals to you more.  Try to imagine yourself in each place (and in each season!).  
Hope that helps, and I wish you luck.  Also, as one of the deans told me when I was trying to negotiate more money: as major as this decision is, all of your options are great, and you really can't go too wrong with whatever you choose.  Reminding yourself of that may take some of the pressure off of this decision.
 

@zling I'm not sure if "snobbery" is the right word, because it really wasn't either of the things you mentioned.  Maybe arrogance?  I had the distinct impression that they were trying to dazzle us with their wealth (e.g. they gave us an impressive swag bag upon entry) and their prestige (name-dropping faculty is normal, but talking constantly about how elite they are compared to other schools, and trying to suck up to us with the same message isn't, IMO).  
Had they done these things with a flawless event I may not have noticed them, but there was remarkably little thought put into some of the proceedings.  The chosen facilities were not big enough for the turnout, and there was literally no comfortable place for us to eat lunch -- most of us had to sit on the floor.  They kept bragging about us being "the most students ever" to attend the event which was downright confusing: they were responsible for inviting us all and had to have a rough algorithm for how many would accept, so they knew what the turnout would be when they were organizing it.  But they talked it up like it was proof of their greatness, when really it just seems like evidence they're trying to grow their program (e.g., perhaps to better monetize their brand?).
So yeah, my chief impression was of them trying to dazzle us but in a rather lazy, even contemptuous, way -- after all, they would have to think pretty little of us naive grad students if they really expected us to be swayed by a fancy water bottle and their legendary name.  (This was arguably colored by my first interaction with them, when someone called me about my acceptance/offer, asked where else I had heard from, and immediately told me "Oh, we're way better than them!")
I will say that when organizers got out of the way and just let their faculty talk to us, the presentations were damn impressive.  Also, I was in a distinct minority of the 300 or so students in attendance, many of whom seemed enraptured if a little confused by the occasionally shoddy accommodations.
 

I think this comes down to what you want to do for your career.  If you know you want to do IR, then Georgetown seems like the place to go.  If you're not set on IR, then few places are better than Harris for an MPP, especially going into private sector outside of DC.  If you definitely see yourself in DC, then Georgetown would probably be the way to go (though tbh Harris's DC network is nothing to scoff at either).
Something to complicate your decision is Harris's relatively new Pearson Institute for Global Conflicts.  They are trying to ramp up their brand in IR as well, and a significant amount of students at their Admitted Students Day were there specifically for Pearson.  My impression (though I'm no expert) is that the Harris brand will open more doors outside of DC, possibly even internationally.  
Have you attended the Admitted Student events at both schools?  Because I think gut reaction is an important factor too.  I was personally pretty turned off at Harris --  I just sensed a pervasive snobbery about the place.  Friends I've talked to in academia have corroborated that feeling.  If you've attended events at both places then you know how they made you feel.  Otherwise, you may try to talk to people who attended each one.