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I recently bought at auction a 12 bore shot and ball gun made by my great grandfather. At some time the stock was broken in the same place as yours and was repaired beautifully. It is a back-lock hammer gun so nothing to interfere with the repair apart from the trigger guard which must have been straightened. As you say, you should be able to repair it with modern adhesives and maybe a pin or two.
I think the little gun deserves a new piece of lumber. There is an artist in italy that woodburns game animals and birds on exotic pieces of wood. I may send the old stock to him and have him turn it into a clock with a fox on it as it is a high grade ah fox gun.
Before starting restocking I tried some high tec. cement. A little blending and touch up of the checkering. Looks ok to me. If it breaks again it will not be at the same spot. I did some testing on some scrap walnut its a very strong bond