Just wanted to add that my kid ended up with enough AP credits that she was able to tack on a second degree and a minor in an unrelated subject, so she will be able to graduate with two Honors Bachelor of Science degrees (dual degrees, not double major) and a minor in four years.
A liberal arts college would not have given her the same number of AP credits and would not even offer all the majors/minors she is pursuing. When finances are a concern but you don’t qualify for full need-based aid, it is hard to beat the cost of state schools. So if the net price calculators at the private schools are not giving favorable results, that is where I would look next.