Leveling drywall patch
Why not use standard 1/2" drywall after you shim out the studs. Use 1/4" stock or rip 1 1/2" strips of 1/4" plywood. Tack these to each stud. Then screw the 1/2" drywall through the shims and into the studs. I would probably use 1 5/8" drywall screws for a better grip.

By the way, if this is in or near a furnace room, be sure to use fire rated drywall.