Personally, I think you should be competitive for all those schools. Your quant is really high. Your verbal is a bit low, but I assume English isn't your first language. Just don't apply to schools that's heavy on English communication like Darden.
One thing I would suggest is to look for schools that is strong in quant and value candidates with high quant scores, like MIT. I think Kellogg, Stern, and Columbia are also strong in quant, so those are good choices. Also, when you apply for schools, you should be a bit more specific on your post-MBA goals and why you chose the goal. It seems that there's a disconnect between your work experiences and your goal. Your work and extra curricula are quant heavy, what demonstrates your interest in strategic management?
You should consider some safety schools. US school's can not provide federal aid to international students, so unless you can get a scholarship and/or private loan. With the economy as it is, loans are hard to come by these days, especially if you are international student. You have a better chance of getting a scholarship at a lower ranked school. Of course, if you can hunker down $150K on your own, then there's no problem. In my opinion, the ultra-elite/elite schools helps when it comes to the more coveted positions like private equity (venture capital), investment banking (probably not anymore), and big 3 consulting. If you are focused on management, I'd say that trans-elite schools will give you almost as good of a education and job opportunity as the elite schools.