Malcolm MacDonald submitted some Free Hands drywall cleats to Cool Tools:
After renting a 100 lb drywall lift for a weekend for $60 to get the largest ceiling panels positioned, I found Free Hands on the internet. They are simple plastic cleats which you screw into the studs or joists to provide a ledge to support an edge of the drywall while you position and screw it in place.
Being at about the same point in our basement renovation, I think I might just have to pick up some of these.