Duke William of Normandy won the battle because was well prepared and had a good army. They prepared carefully for the battle. The Normans had knights on horseback who were skilful fighters.
A utility knife, metal ruler, and a hammer can be faster than trying to carefully saw an opening. Score the drywall a couple times till you are most of the way through, then just knock a hole with the hammer and break the drywall back at the score lines.
Install 1 5/8-inch nails through the drywall into the regular wall studs. Install 1 5/8-inch drywall screws through the edge of this second drywall section, into the back blocker's stud using a screw gun.