I did a repair to a Lefever G grade that had a corroded mass of lead shot stuffed into a hole under the buttplate. It was even swelled enough to distort the buttplate. I dug the shot out and used solvent and compressed air to clean the split before gluing it with Titebond II wood glue. Fortunately, I was able to draw the crack completely closed with rubber tubing, and the repair is extremely hard to detect even though I know exactly where to look. After the glue repair was completely dry, I filled the hole in the stock with a close fitting walnut dowel which was glued in with clear West System epoxy. The shape of the buttplate was restored by softening it with boiling water.
You will need to completely remove the lead before attempting to glue the split stock. And remember to keep any chips, dirt, etc. out of the crack. Try pulling it closed dry before doing it with glue to make certain you will have as undetectable a glue joint as possible. You may actually have to force the split open a bit from the rear to dislodge any particles that would prevent the split from closing completely. If rubber hose or strips of inner tube won't pull it closed, it might help to use rope as a tourniquet. In clean walnut, Titebond II gives me the most invisible glue joint. The only good stock repair is one you can't see.
Edit: To answer your question, the crack probably wants to close up once the stress from the swelled lead plug is removed, so long as there is no debris in the split preventing that. So I don't think it is necessary or desirable to mill out a big opening in the butt, and then filling that with a mass of epoxy. Plus, I found that Acraglass or other clear epoxies did not give as undetectable a glue joint as the Titebond II wood glue.
