My problem was a lack of understanding about how a screw joint actually works. It's not the threads biting into both pieces that secured everything in place. Rather, the strength of a screw joint comes from the threads pulling the screw through the bottom
Measure from the top and bottom of the receptacle to the bottom edge of the drywall. Pencil those dimensions on the upper sheet for the next step. Now prop the bottom sheet of drywall in position against the studs and under the bottom edge of the first sheet.