I’ll bite - this year, acceptance rates at these schools were roughly 5% or less. Your chances of admission are likely to be no greater than that and probably less. You don’t say anything about standardized tests but some of these schools are likely to remain TO for the upcoming admissions cycle.
My kid attended a highly ranked private high school. Most of the kids in the top cohort (NSFs, 99% standardized test scores, 4.0 UW GPA or close to it, good rigor, varied ECs with state and national-level recognition) did well, with most getting into at least one T-20 school, including HYPS, Duke, MIT, Chicago, etc. Most were unhooked. And then there were a few of these very impressive students that got shut out. Why? Nobody knows, except that it’s a numbers game and there is not enough space to accommodate all qualified applicants.
If HYPS is the dream, then give it a try, but keep expectations low and apply to a balanced list so you have choices in the Spring.
Taking on $110K debt is a very bad idea, IMO. And if your folks are covering 2/3 tuition (roughly 40K/year at today’s prices), that four years’ worth of debt is likely to be 160K+, not $110K, unless by “tuition,” you mean total cost of attendance including room and board. Run that figure through an online debt repayment calculator to find out what those payments would be over a 10 year period. It is likely to be eye opening.