Where will you get loans to cover the difference ? Why get a loan when you don’t need one? That’s why aid exists.
I don’t know if you have a shot at getting in, but if you don’t apply then I know you don’t have a shot of getting in.
So why Ivy ? They are tons of great schools and you’d get into tons. There are also non Ivies like Bowdoin that are need blind and meets need and other schools like W&L and F&M that meet need (if they determine you have it) for international.