I was introduced to a delightful product a couple of years ago: MXBon105 that works on most materials. The active ingredient is cyanoacrylate, the same as in crazy glue, but more fluid. Fill the holes with ordinary baking soda (it's basically inert) and pour the MXBon into it. The cyanoacrylate bonds to the baking soda and soaks into the strands of fiberglass as well, locking everything together. It's instant, solid, tough, waterproof, drillable and permanent. You can redrill and use the better self-tapping screws as suggested.
You can check their website (www.mxbon105.com). I'm sure there will be a number of wiser people sneering at this but try it on something before you shrug it off - I was amazed by it and I have no stake in it.