The issue is, you are an excellent candidate, but the schools which meet full financial need for internationals tend to be difficult to get into – reaches.
Definitely still research them and compile a list of favorites based on your priorities, and apply to them. You never know – the only way to have a 0% chance is if you don’t apply. You are an impressive applicant, and you may find a home at one of them.
But also research less selective schools that offer strong aid to internationals. I’d say, private schools ranked, oh, 21st and lower among LACS (check the majors they offer to ensure compatibility), and about 35th and lower among universities, in the US News rankings. As selectivity decreases, your chances arbitrarily increase. The trick is to find some that also offer great financial aid to internationals, or that offer scholarships for which you would qualify.