Neither Does UW-Madison or USC
Depending on your intended major, Cal Poly would be a good addition to your list. It’s slightly bigger at 22,000, but it has the advantages of very small schools. Classes are small and all taught by professors (not technically, because some are not on the professor track, but they all have PhDs) including labs and discussions. The labs in the college of engineering are probably unparallelled for undergrads. It’s in an idyllic location.
I’d add Missouri S&T. It fits your size requirement, it’s a very good engineering program, it has a vibrant Greek system and it’s close to home. Your GPA and scores would make it a match. My sister chose it over MIT. It’s not a MSEP school, but you’d probably get money.
Adding to the money discussion, money matters, because money has opportunity cost. The money you don’t spend can be spent on something else, or even invested.
Good luck.