The BSA commercial bolt action rifle stocks used to use a tapered wooden dowel, across that area of the stock. It was held in with a non waterproof glue, that eventually allowed the dowel to loosen up when the stock/dowel dried. When this happened, the stock would just about always crack in the same location shown in the OP's pics.
If I can find it, I glue the dowel back in place, with a good, clear waterproof, wood glue. Usually, in the process of doing so, enough glue gets into the crack to help keep it together. This makes for very little mess.
The wood dowel doesn't have to be tapered if you're inclined to fit one into your stock and can be finished off very easily and cleanly.
The next thing I do, to make the fix tougher and maybe clean up other issues with a dried out stock, is to make up a "staple" out of a coat hanger, drill a couple of holes in the right places for the pins and then clean out a channel for the cross bar. This is done just under the receiver ring flat, behind the recoil lug.
Once it's in place, I glass the staple in place and bed the receiver at the same time.
Kills two birds with one stone and may even help the rifle to be consistently more accurate.
