Last night, I drywalled most of the inside of the washer/dryer closet with moisture resistant drywall.
It looks pretty spiffy.

My width measurement was a bit off, so the panel was slightly too small.  This made for some wacky cutouts for all the service holes (drain, supply box, electrical and cleanout plug)  I had to fill a nearly 1 inch gap next to the supply box, and the rest of the holes have a big gap to the left of them, but those can all be filled with joint compound pretty easily.

I also am concerned that one of the PVC joints in the drain may be leaking a bit after moving it around during installation - I'll double check that before running a load of laundry through it.