Sounds like the struggle with $$ is going to color your undergrad choices a lot.
See if you can figure out the $$ amount that your family are willing to pay: that is, how much in-state will require out of pocket. One way or the other, that’s your max budget.
If you are indeed full pay for Cornell, then you are chasing merit- which is hard, and getting harder, even with great stats. It also means that you are looking at schools where your stats are worth the college paying for some/most/all of your education- in other words, they stand out from the majority of the student . For a student whose peers are headed to highly selective schools that can feel like a let down. Do the research, but the usual suspects are places like UAlabama, USouthCarolina, etc.
I think you misunderstand “liberal arts” schools. MOST US colleges & universities are on the Liberal Arts model. Outside of a handful of specialized schools (eg Colorado School of Mines, Harvey Mudd etc), there will be very strong humanities presence anywhere you go- not just the top names.
You have a super academic record, and I am sorry that finances are likely to limit your options- but that is the reality for many- indeed, most- students. In turn it is why even at your in-state options you will be able to find other smart, motivated students.