I don’t know how the international specific acceptance rates compare, but Bowdoin’s class of 2028 acceptance rate is 7%, Amherst’s 9% (Dartmouth 5%). I don’t think acceptance rate should necessarily drive OP’s strategy, but it would be one way to make decisions.
That is good news. So no harm in giving things a try in the US, at both need blind and need aware schools. Any might choose to fund you (but all are reaches.)