I suspect you wouldn’t be a fan of the weather at Mudd, but I can see why it appeals in other ways!
Since having Gonzaga on your list indicates that you’d consider Catholic schools, I’m wondering whether you’ve considered Notre Dame. I think it has the engineering/liberal arts balance that you want, with a robust classics department as well as mechanical and aerospace engineering (joint department has both majors) and a physics department with several different concentrations including astro… plus a very strong and inclusive residential college system, a suburban setting, and plenty of wintery weather. And a high-profile marching band program, should you want to keep that up!
Presumably you have been running Net Price Calculators at schools that meet financial need, and verifying that they’d give you enough aid?
For a smaller, rigorous, cold-weather STEM school with a strong residential community, you might look at Michigan Tech. They do have English and History majors, but not Classics. Similarly, Colorado School of Mines might appeal. SUNY Binghamton might be worth a look too. (It’s about an hour from Cornell, if you’re considering a visit.)
You obviously have very strong grades and test scores, and a range of extracurricular interests. Some of your schools are super-competitive, as you know (and I think your matches and reaches are really all reaches, except perhaps for Cal Poly), but you have some good match and safety options as well. So far, so good!