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.

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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.