Hi! Fellow native Tennesseean here and current college coach/advisor for high school juniors and seniors.

I would really suggest Harvey Mudd (part of the Claremont Colleges in California) as a reach school for anyone interested in STEM. It's a STEM school that's part of a wider campus of 5 schools. Harvey Mudd itself is small, but that is offset by the fact that it's part of this network of colleges.

When you look it up, it will be listed as a liberal arts college (which should not rule colleges out for STEM students imo) but it is an intense STEM school, but does have a small core curriculum. This core curriculum will allow you to try on different STEM disciplines before you declare your major (you can't declare until after your Freshman year) and allows all departments to be a little interdisciplinary. For example, a student has told me that they were required to create a computer program in their biology class for a project. Double majoring is encouraged and you can take classes at another Claremont campus.

Your senior year you will plan and execute your own research project or apply to their clinic program, which gives you actual industry experience as an undergrad! More on that here: https://www.hmc.edu/clinic/