You have a terrific profile, great grades and a spectacular GMAT score. The only weakness in your profile for 2+2 is your undergraduate school. I would certainly apply, however. Given everything else in your background, you could make a very good case for yourself.
I think it's also important to note here that if you don't get in, you can come back and apply later. The fact that you showed early interest can only help and not hurt you when you apply with full-time work experience in two to four years.
Good luck to you.