I've only done a couple carbine stocks. My mentor convinced me I would get a more personally satisfying result if I stripped the old stuff off.
He was right. I used a citrus-flavored commercial stripper that basically painted on with a cheap toss-away brush, and waited for it to foam up, then wipe off, I forget with what.
Did a few years ago with surprisingly good results. Haven't gotten around to another project yet.
Good luck, don't be too anxious, it goes way better than you think. I did 0000 wool buff in between a couple buffs with xtra fine sand paper. There was a tool for the diamond grip that I never had to use.