I'm not sure what I can do to help, but I'm happy to answer any questions!
A few thoughts:
My research has also been in applied stochastic processes, so that's definitely a neat area (although I'm at one of the schools I mentioned in my post, so not one you'll be applying to)! I know Columbia has a strong group of people working in this area, stochastic processes, in their IEOR department. I don't know a TON about them, but I think that would be a pretty cool place to be with your interests. UPenn is a great school (obviously), but I wasn't even aware they had an OR deptartment. Are you applying to something in Wharton? If you're looking at stuff like that, maybe you should also consider programs at Columbia Business School (Decision, Risk, and Operations) and NYU Stern (Information Systems). Also, if you're applying to school in Philly, is Boston (MIT) really any farther away? My thought process when I was applying was different from yours, in that I was willing to move just about anywhere to go to the best program I could get into. That's definitely a personal decision, but where you get your PhD/who your advisor is sticks with you for a long time. Sure, if you get into Columbia, then go for it, but if you could choose between, say, Stony Brook and Berkeley, this is something that could have a significant impact on your career. Then again, I suppose this depends entirely on what you want to do after grad school, and it also depends on your priorities. Your concerns about your candidacy are valid, most of the students in my program are international and went to the best schools in their home countries, and the Americans come from good schools. I went to college in the US, and I did go to a good school, but it wasn't an Ivy. On the other hand, assuming you learned the material well during your MA, you know a lot more math than I did when I started my program. If I were on the committee (I'm not), I would take that under consideration. Also, you have research experience and know what you want to study. If you can show that your research interests are complementary to those of profs at these schools, that could help you a lot. Don't waste your time re-taking the regular GRE. I think all that matters is the 800 in math, and I wouldn't risk taking it again and not getting the perfect score.
Anyway, good luck applying! Let me know if you have any questions.