Do you know about whiskering your stock, wetting it to raise the grain and re-sanding several times to get a really smooth finish, this a standard procedure on gunstocks. I don't now about beech, on my gunstocks (walnut and maple) I go to 400 grit, whisker 3 or 4 times, re-sand with the 400 and then go to a grey scotchbright pad that is the same a 00 steel wool.
Try the above sanding test in your barrel channel on a small spot and see if the stain will penetrate, if the BC stain is aniline dye it will penetrate, if it is an oil stain it might not, only a test will tell.