Presuming rest, physical therapy (FlexBar) and technique cleanup all take first priority (as they should), if for whatever reason you must play through the TE and do want to change frames, I'd go with the softest-flexing, lowest-vibration option possible that still gets you results -- between the '22 EZ100 and '22 ATS TT100 310, that would be the TT100 310 by a fair margin; it's going to be noticeably more gentle on your arm:
All of that said, if you can somehow live with the playability, I would give the Wilson Clash and even ProKennex a hard look. If you're willing to consider a frame switch just for the sake of healing, then you might as well turn over all the rocks and go as far as is necessary. Just my 2C. Best of luck healing up your TE.