Generally if doing this kind of repair one would draw as muck of the old oil from the wood as possible. With a good join and modern adhesives with the wood sealed post repair it is not going anywhere quickly. The way I do it is not simply attaching to the broken off section of the bottom ear I chisel out a rectangular section from the head of the stock then soot the replacement wood into place, then clean the wood to remove the soot, whiting to draw out the oil if necessary, scratch up the contact area's to make a good key then glue in place. Cure for 24 hours then re fit for any affected parts.
