Totally feasible; especially for heavies. I got waivered off the street at 36 (technically 37, by the time I started UPT). It’s all in how hard you’re willing to hustle to get there, but a lot of my hustle was in getting the stuff that was needed (test scores, medical, recruiting paperwork, etc.) done before/right after getting hired.
Get your AFOQT and TBAS done (when you’re ready to test); sooner the better. If you get 80s-90s on Pilot, Nav, and PCSM, you’ll get a lot more attention from recruiters and units. You said you needed a medical waiver, which is another huge hurdle and something that might give units pause, so get rolling on going to MEPS and, if it’s possible, try to get an FC1 out of the way to ensure those med waivers don’t hold you back. You’ll have to have that before you go to a UPT board and that takes time.
Get a solid packet together and get working with a recruiter if you’re looking at Reserves options. A single Reserves recruiter can handle any Reserves unit you’re interested in; Guard will have individual recruiters for each unit, which makes things tougher (but still doable; just more duplication of efforts).
It’s all based on your hustle and anything is possible until you’ve heard ”Yes” or your final “No.” Keep networking, keep digging for what you can do next to help your cause, and don’t let any “No” answers dissuade you from trying more options. Part of it all is proving how bad you want it and putting in your own legwork and being persistent will go a long way to showing you’re serious.
Good luck!