Todd,
I, like your drummer might be able to, can play both left and right handed drums, (on either right or left handed drum set ups). I suspect your left handed drummer might be able to do the same, making it very probable to not have to switch around the kit. (In other words, play either hand for the hi hat and snare). The tougher part will be using his feet for opposite playing of the bass drum and hi hat. But if able to use his hands for either setups, he will quickly be able to have his feet play opposite of what he is used to.

OR, make room for two sets,,theirs and his!

OR, make all the right handed drummers play his left handed drum set up! LOL

OR, close every show and just quickly switch the right handed drum kit to the left side.

At practice, ask your drummer to switch hands on the fly playing any beat, and see if he can do the old switcharoo on the fly. If she can, he could play the right handed setups with his hand, with then having to practice his feet switching up.