Financial aid isn’t negotiable. The more prestigious the school, the less reason they have to offer you a scholarship. It’s very common to get “short-changed” at the last minute from a private school, because there’s always someone on the waitlist who’s willing to pay it. It happens every year on this forum like clockwork.
What you need to do is treat all private schools as a “reach” and assume that, even if you get in, there’s a good chance you won’t get the financial aid you expect. Apply to some good schools you know you can afford, and THOSE are the ones you expect to attend. If you get lucky with financial aid, you can consider a private school on your list. Otherwise you risk spending your first year at community college 