I would not trade Gay, either. They can let Mayo go. Sam Young and Allen can cover the 2 guard as can battier who can also back up Gay. But I think Battier is a UFA this off-season, no?
Gay will take his shots from Mayo's departure, and hopefully all the really bad ones Allen would put up (aka 10+ feet out).
Gay would also be a good player to play more minutes along the bench unit which will need scoring punch.
For instance, Conley, Allen, Gay, Zbo, Gasol for the 1st 6 minutes. Then you pull Gay out for Battier for 3 minutes. Then sun out one of the bigs for Arthur and then Allen out and put Gay back in.
bench unit of: Vazquez, Battier, gay, Arthur, Gasol (or Zbo/Hadidi).
And FTR, Gay was +3 on the season in on/off differential per 100 possessions. The team has been +1.5 without him, including post-injury.
edit: Although, I'd try really hard to package Mayo and Conley for CP3. Or Deron. I doubt either has a chance, but it's worth a shot.
Mayo has to go, though. If they can get some other depth or draft picks for him would be great.