I'm thinking someone heavily oiled the rifle and the oil is carrying the rust into the wood like osmosis. I still think
cleaning the iron of rust will stop the process, but getting that oil out of the wood might be tough. I wonder if denatured
alcohol on a cloth would pull the oil out of the wood. It will also pull the dark color out, but if you overdo it, it will be a
problem. I think it's going to be a painstaking process.