Ray: I re-did a stock back in the late '70's and used the gun until 2003 when the left barrel blew. The stock was poor and the oil finish withstood about 20 years of field use with little evidence of being there. That convinced me to re-do a couple other guns (not Parkers) in the same fashion. I have been very pleased with the outcome.
Here is an example of what the stock looked like before being done (not the one I did but one I am currently playing with)
Here is the one done in the late '70's. In the field until 1985 and then again 1995 to 2003 Pictures taken 2006

Process is pretty straight forward.
Strip old finish (chemical stripper or sandpaper, although some are dead set against sanding)
Remove dents and dings if you can. A wet cloth and a hot clothes iron applied to the area can raise some dents.
Get the wood as smooth as you can using ever finer grits and fine steel wool
Wet the wood and let dry. This will lift fine "feathers" of wood
Take those off with fine (0000) steel wool
(I didn't do this but I think I might add a bit of stain for a darker finish on the next one)
The rest is all done with the fingers to apply and the palms to smooth over the entire surface.
Apply a wood sealer (I used Birchwood Casey sealer)
Take down with steel wool
Re-apply sealer
Take down with steel wool
Apply oil finish (I used Birchwood Casey Tru-oil)
Take down with steel wool
Re-apply and take down as many times as you like
Pretty sure I did 20 or more times
You can top that with wax and buff
So there isn't much more to it than that and if you have lots of time on your hands you can end up with a pretty nice end product that will withstand most field handling.
Cheers,
Jack