To the Original Poster-
Honestly man, I'm not trying to patronize you, just offering some (unsolicited :-/) advice-
It sounds to me as if you are tearing up cover songs really easily, picking up new songs really quickly, and that you are a very capable musician; considerate of things like tone, tempo, dynamics, listening to the other members and making sure they don't suck, etc.
Anyway, my point it this:
Even if you do find a decent cover band, I don't think it will be as fulfilling to you as it potentially could be to do your own thing musically. Knowing what you know, I totally think you should start writing your own material!! Find a competent drummer, a competent guitarist, and a place to get together once a week--- that is really all you need man. Sit down and hash out some tunes. Especially if you have an appreciation for GOOD music, classic rock, blues, etc... I bet you could write some face melting stuff. The world is in desperate need of a tight, ballsy original rock band to step up to the plate right now.
Of course, if you're looking for a way to make some extra loot on the weekends, then definitely find a cover band- something will turn up eventually, I promise. I just feel bad hearing how quickly you pick up new material, and hearing about what guys like you, professional musicians, have to deal with on a regular basis. Maybe if you work your schedule out on paper you could find time for a cover band to make some cashola, and a band "for your soul" that may prove to be much more rewarding for you in the long run. In my experience, a lot of venues are actually dying for good, original music. A solid beat, a basic understanding of the blues, and a guitarist with a tuner--- the possibilities are endless.
Just a thought. Best of luck to you, duderino. I hope you find a band that makes you happy ASAP!
{EDIT} FWIW, I'm not trying to say cover bands are better than original bands, or vice versa-- different strokes for diff'rent folks, dig? I've seen some GREAT cover bands, horrible cover bands, great original bands, and horrible original bands. I just thought considering what I said might open up some more windows for you, dig? (I don't usually say "dig" in real life, but it makes me sound cool online, ha!)
[EDIT #2] Congrats on finding some competent players!