Specifically SU, I don’t know. Son is at Tulane (as you might recall). My sense is that while many of the Arch courses are open to anyone that wants to take them, the studio courses are almost entirely the students in the BArch program. The studios are 6 credits, 3 classes a week for 4 hours/class. My sense looking at other college curriculum’s for the BArch programs is that it’s pretty similar - so I wouldn’t imagine someone from a different program taking the studio.
Lots of great suggestions/options given by others… Agree that one of the bigger hurdles is the financial one. If you’re unlikely to qualify for any aid beyond merit and you’re looking at ~$40K/year, it’s going to severely limit your options. Not to suggest it should hold you back from applying to wherever you want and see if you get the merit offer.