Anybody know of any MBA programs that still have their applciations open for the fall 2016 intake?

Fall 2016 intake would still be open on rolling basis for native citizens.

I don't know, looks like most of the top MBA programs' application cycles are now closed:

http://find-mba.com/news/2015/06/upcoming-mba-application-deadlines-for-fall-2016-us-business-schools

But some schools may have extended their deadlines beyond what's listed there. I was just looking at the Rutgers site and it said that they've extended their deadline until June 15. So it's probably best to check with the schools you are interested in applying to.