You have a very strong background but your work expereince is too short. You might want to consider work for another 2 years before applying for S16. That said, you might want to give HBS a try since they like young and talented people such as yourself.
Not sure about MSF to be honest. But I don't think an MSF gives you the same career reach as an MBA (I could be wrong). Also, I would suggest that you think hard about "Why you want an MBA?" It seems that you are more interested in stay in the US (which is fine of course) but there are many other ways to do that. As we both know how expensive an MBA can be.
Only target at those best schools (MIT LSE Princton). others are not worth the time/money. but your age is against you to find entry level non-quant position in finance.