Several people suggested using Resilient Channel (or Z-Channel) to hang the drywall. I was on the fence about using it due to some installation concerns, but when I contacted John Callen the drywall hanger, he said "I use it all the time. It's great stuff; I can hang it for you no problem." Case closed! Here you can see the bare channel and the standoff it creates when the sheetrock is hung from it.