Not knowing just how wide the gap is, this technique may be too extreme but here goes. Take another piece of walnut either from a donor stock or a walnut dowel of sufficient diameter and work it to “rifle barrel” shape and epoxy it into the barrel channel. The glue line should be very small, if done properly. Then proceed to inlet a new barrel channel. Stain and finish. I have used other hard woods but you have a better chance of the stain matching with real walnut.
I'm thinking if I use a filler that doesn't absorb moisture, then there is less chance of the stock swelling up in continual bad weather and I don't think I would be able to do a good enough job using another piece of walnut for it to look ok, unless I gave it to a stock maker to do.
