I am going to be a downer here. If your EFC is $35,000 and your budget is max of $20,000, you are are going to need to include realistic financial options. For example, Case Western might give $30,000. That sounds fabulous, except for the fact that cost of attendance is $60,000 which leaves you with a $10,000 gap. They offer a few full-ride scholarships, but they are only a handful. A “few” is going to be the scenario for almost every single full-ride scholarship at the higher ranked schools. They are much fewer in number than most students realize. I don’t know what the NPC would show for HYP, run them and see. But, statistically, these are all apply and hope for the best, but you need to be prepared for possible disappointment in terms of financial feasibility and/or admission (in terms of HYP) {Just room, board, books w/o tuition can run $10,000. So it is possible that 1/2 of your allotted amt won’t even be paying tuition.)
Believe it or not, there are probably more top students in your situation than not. Bc that is financial reality for so many students, you can find intellectuals who love talking theory and philosophy both inside and outside of classrooms on campuses that are affordable. Some of the lower ranked schools will offer not only you lots of merit $$, but plenty of other kids just like you, so all of those students are enrolled on those campuses due to the exact same scenario. These schools are not intellectual wastelands.
FWIW, I know the above occurs, b/c it is our kids’ reality. They have found their tribe and have loved their schools.
Look into honors programs within honors colleges. The program our ds is in focuses on research and he loves it. They accept 40 students per yr and they are offered fabulous opportunities. Our ds is the deep thinker type (loves physics, astronomy, philosophy, theology, math theory…and literature) and he has a great group of friends who are all as academically oriented as he is.