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I have a similar situation that I am going to have to deal with.. I have used JB weld on the dash panels, the holes on the sides were about the size of a dime (all the fiberglass was cracked out). Filled in the area with JB weld and then drill another hole just big enough for the screw. Used a vinyl repair kit for the side that shows and from a few feet away you'd never tell unless looking for it. I am thinking about using a simiar method on the my door panels. Thinking about shoe-goo to fill in the area missing, this way it will still be a little forgiving like the original pressboard back (JB gets really hard), then the vinyl repair kit on the front to cover it up... Hope this helps. :seeya
It's kinda like liquid rubber in a tube. Should be able to get it at a sporting goods store, bought mine at Walmart. It's used for repairing/rebuilding the soles of sneakers. It is very similar to the filler they include with the vinyl repair kits .
Ed T -- most of the suggestions you have received will work for repairing door panels. Most problems with the stock panels are due to the material used to make the panels--it's essentially paper and doesn't have too much strength on its own. Replacement panels from the aftermarket providers use an ABS plastic to which the interior material is glued. Before installing your repaired panel, put the plastic liner back on to keep moisture away from the back of the panel. If the stock liner is long gone, you can make your own from 10mil plastic available at most home centers.