Thoughts on my chances at Mfin for top schools like Princeton, MIT, NYU?

I'm currently applying to masters in finance programs, with MIT, Princeton, and NYU as my top choices. I wanted to know if my chances are decent:

- GRE: 169 quant/168 verbal/6 writing

- 3.8 GPA from a top school (think Harvard, Yale, Princeton, Stanford) but degree was in the humanities. 

- Worked at a top hedge fund for 1 year straight out of school. Left to take a few courses in math at good universities (e.g. linear algebra, probability, etc) to get ready for the masters in finance. Expect to get either three As or 2 As and a B+. 

- Strong recommendations from a pure math professor and a econ professor in high level courses where I did very well (just didn't take many of that sort) attesting to my quantitative strength.

- Otherwise, very strong extracurricular accomplishments from undergrad (national/global recognition). 

I realize I'm a bit of an oddball candidate. My understanding is that many MFin applicants are from abroad, study quantitative subjects, are sometimes looking to get a brand name on their resume so they can go to a hedge fund. I am from the US, studied a quantitative subject, and am coming from a hedge fund and a brand name school. I am taking courses now to fill in the gaps in my knowledge. If I do reasonably well in these courses, given the rest of my record, what would you say are my chances?