Why do you think this is so? I’ve spent more time looking at Yale than Columbia, but the Ivies will generally make some level of need-based aid available for most families with incomes up to $200k, albeit on a sliding scale. My own family income is slightly higher than OP, and the NPC indicates that my D22 would receive substantial aid from Yale, bringing net cost down to about $17k. I haven’t seen anything to suggest that international students would receive aid from this small group of elite “need blind/meets full need for intls” schools by some different method, though I guess that’s possible. Obviously each financial aid situation is unique and there are no guarantees, but I think it is plausible that Yale would be within OP’s 20k budget if she were admitted. Pomona also has generous financial aid (our NPC net cost was only 5k more than Yale), but I believe they are need-aware for admissions.
As I recall, Amherst is need-blind/meets full need for international students, so that might be an option for OP also.