I can only chip in with regards to the math question. You definitely do not stand a good chance at the programmes listed. A solid GMAT score (like yours) serves to reinforce your mathematical prowess demonstrated during your time as an undergrad or grad student. It can't be used as a substitute.
I'd suggest you revise your expectations of the programmes you can realistically get into, simply because these top programmes get a lot of applicants, so you can't afford to slip up in any area, given that there are very limited spots available and you don't have anything unique (like extensive RA experience) in your profile that nudges them to pick you, over another candidate with good grades + good GMAT. The best guage of your competitiveness is to speak to your professors. They will be more familiar with the admissions process, although they'll expect you to do your due diligence before approaching them.