I have glassed in a number of "G10" backing plates of varying thicknesses. I used West System epoxy with their high-strength thickener. Rough up both sides (G10 and the receiving surface) with 16 grit. Use a right-angle sander/grinder and aim the out-fly into a 3" hose end of your shop vac.
Cleanse it with acetone.
That's one High Strength bond!
Note that sometimes the vendor will have G10 listed as G10/FR4. Same stuff.
If you are outside of a metro area with a plastics supplier, you can get it on-line from McMaster Carr.