Since you’ve visited schools in Iowa I’d assume you’ve looked at Grinnell. If you have your heart set on not taking the public option, that may be the best (or close to) fit for what you’re looking for. Obviously, you should contact the coach to figure out athletics, but I’d say that Grinnell has strong academics (biased to an extent bc current student) and pretty regularly gives out merit aid at around 20K+ a year to domestic students. I don’t know any pre-dental students, but the bio program is great and the pre-meds I know are pretty happy. I also personally think the student-athlete experience has been great. With your stats, I’d say you would have a strong shot at ED, but that is a financial gamble (though if you’re recruited, the coach will likely encourage ED). With RD, I’d recommend demonstrating lots of interest in the school to maximize chances of acceptance.
Perhaps not a top choice if you’d like to leave your hometown, but applying to Macalester EA would probably give you an early acceptance with some merit.
As far as I know, Grinnell and then Mac seem to be the highest ranking schools to frequently give large merit aid and meet your other qualifications. I believe Kenyon gives it out fairly often, but many of their sports teams are incredibly competitive (no idea about tennis). Oberlin also gives it out, but in lesser amounts (website says 10K guaranteed).
East coast will have very few competitive schools with merit aid. Most campuses out East seem to follow a pretty bimodal distribution of wealth (most are very wealthy or very poor, and then a few in the middle). At least that was the impression I got while visiting.
Best of luck!