Just curious what the sheetrock plan is. My first idea would be to glue 1/2" Type C over what's already there. I don't know of any thinner fireproof sheetrock, but there may be some. On the walls, that would even eliminate any fastener mudding. In our house that we live in, I glued a layer of 3/8 over 3/8, and had no fastener heads in the fields. I wouldn't even worry about field fasteners for the ceiling if glued with Powergrab and installed with a modified sheetrock lift.
I know it's not your job, but faster and easier would be good for all.