You should scratch the jazz itch if you can. And also do a cover band. You may find songs that you aren't really interested in listening to for fun, might end up being fun to play in a band, or at least just engaging enough to enjoy as a part of a band putting on an engaging show, song by song... IF you have the right people that can all be on the same page and similar skill level.
I know this as someone who has a degree in classical music and has done everything from play basements, backyard barbeques to clubs to world-known concert halls and all kinds of styles. It has been true for me that some music I don't really care to listen to (The Bachs, Beethovens, Brahms, Traditional Jazz, Classic Country, Sweet Home Alabama, etc...) in the right situation with the right people, to perform some of this music ranges from a pretty cool blast that I really enjoyed to kinda fun, and at the very least mildly engaging and a way to spend some nice time musically communicating on stage. I think that's a really important point and why I expounded on it.
In general, I'd say keep enough ego to know or believe you belong on stage doing well and putting on a great show, but otherwise let as much of the "Well I'm not ever going to perform X for Y reason" go by the wayside as much as reasonably possible. Have standards and expectations and to strive to differentiate yourself in a marketplace of cover band music, but also have latitude and flexibility to TRY some things at first glance which you might be less than enthusiastic about.