Dr. Tim,
Though I haven't used this technique on a longrifle or fowler stock, I HAVE finished a couple dozens of "modern" black walnut stocks (19th century cartridge rifles). Here's what works for me:
I sand the stock thoroughly to 400 grit, and whisker at least twice (more if it needs it) then burnish with a fine grey Scotchbrite pad. I seal the stock, including all the inletting and underneath the buttplate with 2 or 3 brushed on coats of Pro-Custom Oil Finish (Brownells) thinned about 50% with mineral spirits. I want this to penetrate as deeply as possible. Depending on climate (I want this to dry completely) I let it dry for 2-3 days.
Next, I use the same finish full strength, and rub on a couple of coats, a few hours apart...I let the finish set to the point that it isn't tacky between coats. This is allowed to dry overnight, then wet sanded starting with 400 grt, using the finish as a cutting oil. As I sand a section, I wipe the slurry off cross grain, with a clean paper towel, trying to leave as much in the pores as possible. The stock is then set aside to dry overnight, and the process repeated with finer grits.
It usually takes me a couple of wet-sandings at 400, and a couple at 600 to fill all the pores. Then a couple of very thin coats are hand rubbed in to finish things off. A rub-out with a very fine Scotchbrite (mine happen to be white), and a coat of Johnson's Paste Wax and it's ready to go.
This is a very durable finish...one of the "oil modified urethanes" or some such...similar I think to Permalyn, but I prefer the Pro-Custom because at the normal humidity levels here in east Kentucky, it gives me just a bit more working time than the Permalyn, and seems to be a tad thicker product, which helps in the grain filling process.
Greg