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 two rectangular pieces of drywall the width of the doorway and as deep as the arch. The drywall should be as thick as the one on the wall, usually 1/2-inch thick. Hold one drywall piece in the door opening and scribe the outline of the arch on it. Cut out the arch using a drywall saw. Use this cut piece as a template to cut out the other drywall piece. Screw one cut drywall piece to one side of the arch with the plywood forming a support.