"John" wrote in message ...
The screw simply go into pretty thin fiberglass; there is nothing behind the
fiberglass. The screws have simply stripped out the fiberglass. I can put
down a couple new layers of glass, but I expect it will just strip out
again. There is no access to the bottom to add a backer.

I don't know what they are called, but what about using the screws
that you use for hanging picture frames on a plaster wall. On a wall
you drill a small hole in the plaster, pound the screw into the hole
with a hammer and then as you turn the screw the metal sheath deforms
and creates its own backer. Seems like it might work in your case.

Bob