Its an interesting question. The big unknown, is what is the benefit of a rest? Is an unresteded Josh an 80% version, and a extra week rested Josh 100%. If that ere the case, I would rather be on the road with 100% Josh in the wild card round, than home with the 80% Josh. But I doubt an extra week makes that big of a difference. So just play Josh and try to win the game, would be my strategy.
Completely separately, not playing Josh and losing, then losing on the road with a rested Josh in the first round of the playoffs would probably result in fans calling for McDermott's firing.