You already have some good options and some good suggestions above. I’ll add a couple more.
Your profile fits well with that of admitted students at Colgate University, a small (3100) liberal arts college in upstate New York. Like all similar liberal arts colleges in the Northeast, they say that they will meet 100% of demonstrated need. They elevated their profile in that regard just a couple of years ago with something they call the Colgate Commitment. Check it out on their website to see how your family income corresponds with what they will award for your need.
Two members of my family have gone to Rice (4600 undergrads). They seem to be particularly holistic in their admissions as we were surprised when our GS was admitted. It isn’t on either coast and it is in the South (Houston), but it’s different and is much more like a Northeastern university. In fact, they modeled their housing plan on Harvard and Yale with the specific intent of building community. They too have a published program explaining how they meet financial need. It’s called the Rice Investment. You can check it on their website to see how your need matches up. Rice is more selective than Colgate, which is in itself highly selective, but I think it’s worth a shot.