@brantly, the parents have to cooperate with FAFSA and CSS Profile for the OP to get need based aid. So she does need them on board.
OP, Mudd and UChicago both “meet need” – and sometimes colleges do preferential packaging (provide better aid) to students they want the most. As a URM with great credentials, that could be you. And my kid got better aid from UChicago than some of the other schools discussed here.