Fill the existing hole with two-part epoxy and wait for it to fully cure. Drill a new lead hole the size of the shank on your existing screw. Coat the screw threads with wax and carefully turn it in. It won't be much more solid than the original, but at least you have some virgin material for the threads to bite - you have to be careful about overtightening that screw. It also helps to tighten down the action bolt (at the fromt of the trigger guard) first so you get a good sense of the amount of tension for installing the rear screw....
Elkbane