You need what the muzzle loader guys call a patch worm. It is a screw on a rod that is used to pull patches and balls from muzzle loaders after they fail to fire. I have made them by welding or silver soldering a large sheet metal screw onto a piece of steel rod. For your application, I would try a #12 sheet metal screw on a piece of 1/4” rod. You should be able to screw the screw into the soft lead without a pilot hole. Once screwed in, you can grab the rod with a vise or vise grip pliers and pull the slug out. The hot lead should not have bonded to the wood and hopefully will slide out.
If that fails, drilling is the next option. Using a torch to melt the lead out would probably destroy the stock.
Just had another thought, if you know a body man, they use a similar tool to pull dents out of body panels. It is the same tool I described building with an attached slide hammer.
