Rent a drywall lift for a day.

The repair will be better if you have 2x lumber around the perimeter of the patch to attach to.

Sisters and cross bracing as appropriate, set so the patch wil be flush with the existing drywall.

Upi can even use 2x2 pieces that are longer than the opening dimension and run drywall screws through the remining dryall to secure them in place a tthe edges of the hole.

Try to get at least 1 inch from the hole edges, and them another screw about 5 inches form that on.

The 2x2 needs to be 16 inches longer than the opening.

Fasten the ends of the shorter piece with screws at an angle into the longer ones. Do NOT try to nail into a 2x2 secured this way (even to fasten the ends of the shorter pieces between the longer ones).
Just screws.

The 2x2 should be half on the old drywall, half on the new the 1.5 inch way, and screwed into both pieces about every 8 inches.

You can get by with adding 2x2 pieces.

Seriously, brickeyee, all that for a hole that is 3 inches x 4 inches?

Hold the wood with a temporary screw inserted into the center of the wood, or use a piece of wood that's thinner than the width of the hole so you can hold it in place with your fingers. I prefer plywood scraps since they don't split.

Yes, that's what I'm doing, I can wrap my hand around the board, but as I explained, I can't hold the backboard tight enough to allow the drywall screw to go in. The screw is not going into the backboard, it's just pushing it up.

No hardwood. Softer wood (pine), plywood...or predrill what you have.

The problem with predrilling is that the board can too easily move out of line. That's why I was considering using glue.

You're over thinking this. Just find another piece of wood and be done with it.

This post was edited by homebound on Mon, Feb 11, 13 at 12:25

I worked it out. For the benefit of anyone who stumbles across this in the future, I used a softer, thinner piece of wood for the backing, I used shorter and narrower screws, I predrilled the holes in the drywall, and (most importantly, I think) I put the screws in manually instead of using a drill.

The backing wood is a piece from a long paint stirring stick that was twice the thickness of a normal paint stick.

I taped and mudded and I'm on my way.

This sites software routinely changes single quotes to doubles, or double to singles.

For a 3 in x 4 in hole just put a piece of 1x2 across the opening on the far side, a single screw in the ceiling to hold it in place at each end of the wood, then two screws to hold the patch in place.

Tape and mud.

If you use Easysand20 you can be done in an afternoon.

Drills without screw setting noses are a mess ofr drywall.
The setting nose create the correct dimple for filing to hide the screw head.

The setting nose release on screw depth, not torque.
Regular length drywall screws can stick out of the back of the wood without issue.