@URC2020 For what it’s worth, I didn’t take my first FA package. I appealed with a letter, saying that I could not take on the additional financial burden when compared to the state schools I was considering. They came back with ~$5k more per year to match the cost. I know that’s not in the same neighborhood of what you’re looking for, but there is (or at least was) an appeal process that yielded better FA. Many others that I know also received generous aid without having siblings in college. Without having details on your income, I can’t say why they are not meeting your needs.
At any rate, no undergraduate degree is worth paying $200k+ out of pocket IMO. I was pleasantly surprised when I received a favorable FA package from UR but was prepared to go to cheaper options because it just made sense. Like @Creekland said, find schools you like, see what they offer, then pick one.