Rob,.... if it was me, I'd add whatever wood it takes to get the LOP I'm lookin' for, then wrap it with rawhide and call it good.
I mention this because my interests center on weapons, accouterments, and camp gear revolving around the "western fur trade era",.... and rawhide was the most widely used gun "repair" readily found in the west at that time.
Examples can be found in many museums, demonstrating how rawhide was as useful "then",... as plastic is today.
Looking at a gun's butt
, any rawhide wrapped as I've described would be an indication that a native might'a removed the gun's original butt-plate and used it as a "tool" for fleshing hides, or made it into arrowheads (both of which they historically did
).
Wrapping the gun's butt with rawhide would not only be "period correct", but it also protects the stock's butt from the ground (when loading) and strengthens the stock's "toe" almost as good as an actual brass, or iron butt plate does.
In your case, a rawhide wrap would also hide the "seam" where any added wood is fastened to the stock.
When using rawhide in such a manner, I'd give the rawhide (after it dries) a coat of Tru-Oil to help protect it from getting wet during inclement weather.