Would you please explain the mechanism by which lead shot 'swells' and exerts enough pressure to split the wood? For sure it oxidizes, carbonates and reacts with tannins etc in the wood but why wouldn't those soft surface compounds expand into the spaces between the shot? I've seen wood split over a lead plug in the stock but the cause seems to be drying and splitting of the thinner sections of wood on the horizontal axis of the plug, not the lead swelling to increase in diameter.
OK, although I thought I had already explained it. Simply stated, oxidized lead occupies more volume than lead which is not oxidized. Lead shot has a lot more surface area than an equivalent weight of a solid plug of lead. Therefore, lead shot has a lot more potential to swell sufficiently to split a gunstock than a solid plug.
A similar thing happens with rust, or iron oxide on steel. And this is why you see rebar on construction sites coated with a green epoxy. Uncoated rebar rusts and swells, and actually breaks the concrete used in bridges and road surfaces. This also partly helps to explain why rusted nuts and bolts become so difficult to unscrew.
As an example, a few years back, I saw a G Grade Lefever on Gunbroker that had a long clean split from the buttplate about half-way to the grip. The stock was split on both sides. It looked bad, but it didn't appear that any wood was missing. The photos also showed that the buttplate was bulged outward. I immediately suspected that this was caused by a gob of oxidized lead shot, because I had seen this happen to other guns. The gun was otherwise in very nice condition, but due to the defects, I got it very cheap. When it arrived, I pulled the original Lefever buttplate, and my suspicions were confirmed. I had to use a drill to help break up the mass of oxidized shot. This mass of shot was extremely oxidized and solidified. There was lots of white lead oxide powder, so this work was done outside. I dug and scraped out all traces of it, and used compressed air to make sure there was no debris in the split wood. I glued the split with Titebond II wood glue and used rubber tubing to pull the crack completely closed. After the glue set, I turned a hardwood dowel and glued it into the hole where the shot had been, using epoxy as an adhesive. After refinishing, the repair is virtually undetectable. I had to heat the deformed buttplate with boiling water to soften it and restore the correct curvature because the swelled shot had pushed it outward. This was one time I was extremely sorry that I didn't take the time to take some before and after pics, and especially some pics of the heavily oxidized and swollen shot.