Stanford has historically de-emphasized SAT scores in favor of intangible factors like essays, which is why its average SAT is lower than its peers and why it requires more essays than them. I'd say GPA tends to be more important. Since you don't have much in the way of ECs, and since you're an international asking for aid, you have a very small chance of getting in, unfortunately.
According to this site
, the only LAC that's need-blind for international students is Amherst, although Dartmouth is very much like an LAC. Williams used to be need-blind for internationals, but had to change the policy; perhaps it will change again by the time you apply, since college endowments have supposedly had about a 20% return on their investments this year.