If you can't access it from below, cut a 2 inch strip off one side and slip the plywood with Gorilla Glue on it into place from above. Use a couple of long screws for a handle to hold it up, then pull it up into place with the drywall screws. Be sure to drill holes for the screws beforehand, so they won't push your support piece away.
Once the lower support is in place, just glue and screw the piece you cut out back into place.
Let the glue cure for 24 hours, and you will have a good solid joint with no flex.
Happy Glamping.Norman, 2008 Winnebago Adventurer 38J, W24, dozens of small thirsty ponies. Retired after 40 years wrenching on trucks! 2010 Ford Ranger toad with bicycles or KLR 650 in the back. Easy to spot an RVer, they always walk around with a screwdriver or wrench in one hand!