Yes, getting merit aid from out-of-state flagship publics can be very difficult. It is less difficult at non-flagships. But regardless, for each school I indicated what percentage of students received merit aid and indicated that the cost potentially/might get after merit aid. I would suspect that with OP’s GPA and AP scores would figure out that if only 7% of students are getting merit aid that her chances are much slimmer than if 93% of students are getting merit aid.
I also agree that private schools are often more generous with merit aid than their public counter parts (see DePaul and Loyola Chicago on my list above). As OP indicated that she wanted larger universities, I think I put 8,000 as the smallest undergrad population, which eliminates most private universities. Should she decide that a medium or smaller school is worth considering if it gets her more of what she wants at a more affordable price, there are certainly many other schools that could be mentioned.