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 drywall to fit the areas that you removed on both sides of the arch. Allow it to overlap the arch along the bottom by a few inches and nail it in place on both sides. Use a reciprocating saw to cut the drywall along the bottom following the shape of the arch. If you have some ragged edges, sand or file them off.