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.
Cut the 1/2 drywall to size and cover both sides of the frame. Use the screw gun and 1-1/4 drywall screws to attach the drywall, screwing it into the studs, which are 16 apart. Make sure the top edge of the drywall is flush with the top of the top plate. Mud, tape and sand any seams. Cut the 1x6 clear pine cap to length.