this is the easy way
put duct tape over the holes and surrounding area, redrill holes with a bit at least twice as larger as the screw, larger if possible. Try not to drill all the way through the back of the glass, if you do put duct tape over the bottom of the hole. As you drill, examine the material coming out, if wood, does it look fresh. Scrape out all the surrounding wood with a nail bent to fit in the hole, you can put the nail in a drill, but be careful. Mix up some epoxy and fill the holes being careful to get the air bubles out, this is the hardest step, using a syringe is great. When hard almost, remove tape, take a razor and trim the epoxy. When hard, redrill for the screws, bed and be satisfied that this is a job you should never have to repeat.