We have (had, I guess) a glass shelf in our bathroom, with glass holders
mounted to anchors in the drywall. One came loose, and eventually the
hole in the drywall became to large to set the anchor.

Because of the unique glass holders, I cannot use a larger anchor, nor
will toggles work with the screw I have to use. Relocating the hole
would be problematic. So now I want to patch the drywall and restore
the quarter inch hole.

My plan is to use mesh on the back of the drywall, fill the oversize
hole with plaster, then redrill. I've had good results using this
technique for patching, but I'm a bit concerned that the new hole I
drill will be almost as big as the oversized hole, and the anchor may
not hold. Years ago, I think I heard that wood glue can be mixed with
plaster to form a stronger surface, but my bottle of wood glue says
nothing about this.

So my question is whether mixing wood glue with the plaster will give a
stronger repair and, if so, about what portion of wood glue to plaster
is appropriate.

I'm unhappy, because a few years ago we had two hardware stores near us,
either of which would have provided good advice, but Home Depot has
driven them out of business.