“with a strong stem focus” doesn’t mean it has to be 50% engineering…
Based on your SAT scores, UAH and UA could be affordable options, as list above.
Two of the more affordable OOS engineering options, in Florida, are USF and UCF.
University of South Florida is in Tampa and offers generous OOS merit based scholarships (some of which stack).
https://www.usf.edu/admissions/freshmen/admissions-scholarships/nonflorida.aspx
For example:
USF Green & Gold Presidential Award
$48,000 (up to $12,000 per year) 4.00+ GPA and
1340+ SAT (Evidence-Based Reading/Writing and Math) or 29+ ACT
USF doesn’t offer Aerospace Engineering, but they do offer several other degrees, including Mechanical.
USF’s ROTC program:
https://www.usf.edu/undergrad/programs/rotc.aspx
University of Central Florida, in Orlando, also offers generous OOS merit based scholarships. See their forum for examples. UCF does have a large aerospace program (the school was started in the 60’s to support NASA).
UCF’s AFROTC program:
http://airforce.ucf.edu/det159/
FSU has a smaller engineering program, and doesn’t offer Aerospace, but they could offer you an OOS tuition waiver (bringing your cost down to the low instate rate of $6,300+ a year), based on your test scores.
FSU’s AFROTC Program:
https://airforcerotc.fsu.edu/
UF has the best engineering program in the state (and has a large Aerospace program), but they offer little in the way of OOS merit or need based aid, so it’s likely too expensive. However, with a ROTC scholarship, it could be your best Florida option.
http://rotc.ufl.edu/
I would recommend using the ASEE online (Engineering) program profile to get a more detailed look at any engineering program.
http://profiles.asee.org/