Honestly I think you might have more options if you DID do formal this fall. Yes, you will probably be immediately released from some. But there aren't that many sororities that do spring recruitment at UT. Unless you would have a serious problem with the rejection, do FR. However, recommendation letters are a MUST for all the chapters. If you do FR, start on that NOW. Even if you don't do FR, it might help your chances in the spring to have letters for the chapter(s) who recruit in spring.
Don't forget that FR is before school starts, and you will need to register early. And just don't talk about your age to the other girls that are going through. If an active member asks you, have a prepared answer for why you waited four years and why your experiences in those four years will make you a good member (things like your service activities, etc.) DO NOT imply that you will be the "mother figure" or that you can get everyone in the pledge class beer since you will be of age. If you don't focus on it, they won't focus on it. If you talk about your great qualifications (whatever they may be), that's what people will remember. Not that you are 22. Make them remember you as the girl who spent 4 years volunteering in the jungle rather than the girl who is older than they are.
Something that you didn't mention but that you should be prepared for is to discuss your availability for sorority events and such. One of the reasons upperclassmen and older women are often passed over is that their priorities can be different. They may have a different level of commitment to outside employment, to family, to a boyfriend/child, etc. You are considered a non-traditional student. If you can demonstrate that your involvement will be the same as traditional students, that will help.
The UT Greek scene is an active one, and there is ALWAYS something going on to participate in. Some chapters REQUIRE this participation. If you can commit to being 100% active - for four years - then your chances of getting a bid (fall or spring) will be better.
I know this is long.
Sorry about that! If you keep an open mind, consider all the options, and don't get insanely depressed when you get fewer invitations than some other girls, you have a decent chance. You never know until you try! Good luck!