I believe that Master Minds, Season 2, was filmed during the summer. I remember seeing advertisements for contestants sometime last spring. I suspect that the entirety of season 2 is already in the can.
Assuming Jeopardy! keeps to the same schedule it had before, it only records two days a week. Ken could conceivably work on The Chase and Master Minds on other days. On The Chase, in particular, he wouldn't need to be there for every game, since he's one of three chasers, and only one chaser plays in a given game.
Back in the old days, when there were a lot more game shows on the air, guys like Bill Cullen or Wink Martindale seemed to host several shows at the same time. It's a matter of scheduling, I suppose, but I think it's feasible to work on more than one show at once.