I really like your list. The only one I’d remove is St. John’s, which is pretty mediocre for classics. Consider replacing it with Holy Cross.
If you’re female, definitely take a look at Bryn Mawr.
Brandeis might suit you rather well, I think. It’s small for a university (3600 undergrads), very good for ancient studies and biochemistry, and has an unusually high transfer admit rate (~40%). It’s a bit more “nerdy” than some of the other selective private universities.
Since you’re open to public universities like Michigan, UNC Chapel Hill is exceptionally strong in classics and political science and is also strong in biology. It’s one of only two public universities to meet the need of out-of-state students, and it’s much easier to get in as an OOS transfer than as a freshman.
Many of the other top private universities not on your list - Stanford, Duke, Hopkins, Penn, Wash U, etc. - are great for all of your academic interests. Classics courses will all be very small at all of these. Biology courses are often large at the freshman/sophomore level, but you may be beyond those if you’re coming in as a transfer student. The downside is that they’re extremely difficult to get into as a transfer applicant.
With all due respect to Hamilton, it’s unremarkable with only 3 full-time professors in classics. There are markedly less selective LACs with stronger programs (e.g. Rhodes has 7 classics profs on faculty). That said, students majoring in classics for fun don’t need to be as choosy as those aiming for PhD programs in classics.