Coot: Seal the stock's barrel channel well with stock finish( staining if you want, first). Then consider using some kind of non-petroleum grease to fill in the channel when the barrel is put in. You want the grease to ooze out the top. I would also put the grease on the underside flats of the barrel, since you are basically trying to add a rust inhibitor to the barrel, rather than being concerned totally with sealing the wood. The stock finish should do that. By All Means, go ahead and put a good coat of wax on the stock finish before using the grease on the barrel.
There are all kinds of synthetic lubes now available with a wide temperature range. The draw-back to petroleum products is that the temperature range where they remain stable is limited, both heat and cold. Oils do evaporate out of grease, and when the grease hardens, you lose its sealing characteristics. If you decide to use a grease in the barrel channel, stick to the synthetics. Oh, I have been using " Wonderlube " to protect my barrels during storage, and use. I am impressed with its ability to leave a slightly greasy coating on the barrel, even after heavy use, making clean-up of fingerprints, dirt, and debris from powder much easier.
The only petroleum based grease I have found that seems to defy normal functions, is Water Pump Grease. But, I would not want to leave a gun out in the Texas sun on a 95+ degree day with even water pump grease in the barrel channel, for fear I would have a real mess running out the barrel mortise.
Look for synthetic lubes designed for use in airplane engines, as they require the widest range of temperature tolerance . Temperatures range from very hot, because of the heat from the engines, to -60 degrees, and colder, at altitudes.