From the sounds of it, you should be able to get accepted somewhere. I would not lay odds one way or the other on Princeton, Harvard, or MIT, since I have no idea how they make their decisions, and they get many, many more applicants than they have openings. But that does not mean you should not apply to them. You never know.

You talk about paring down your list, but you only list nine schools. Why not apply to them all? My own mentor advised me to apply to "at least a dozen" schools. One disincentive is the application fees, which can add up. Are you financially strapped? Can someone float you a loan for the fees if necessary?