That's what the Muir Woods if for, Andy!
Seriously, I used my cross bike for commuting last year, didn't run enough miles during the season to wear out tires, but i got pretty tired of pulling off the rest of the commuter stuff (fenders, cages lights....) on Friday night and replacing it all Sunday night. That is a big part of the reason I bought a new commuter, so the cross bike could become pure race and trainer.
Buy a new rear tire, only ride the Jake on days you have cross stuff going, and use one of your other bikes the rest of the week. Cranking that heavy Muir Woods is good training
