If the wood stock isn't stiff enough to hold shape, throw it away and get a decent piece of wood. I have never had an issue with the forearm of factory wood stocks being flimsy. Tupperware (injection molded stocks) that's a different matter.
If I needed to stiffen a forearm, the best way is to use a solid carbon fiber pultrusion rod bedded in epoxy with chopped glass added to thicken the epoxy.
All the fibers run the length of the rod so it has the maximum stiffness. I'd use at least a 3/8" diameter rod, 1/2" would be better.