Another thought, which I broached here several months ago, but haven't had the time to try, might be to boil the barrels after degreasing. I have a couple guns with very evenly brown patina barrels, including a Baker Batavia Leader which has very nice wood and about 75% bright case colors. I wondered, since the original rust blue which is a black oxide (ferro ferric oxide) evenly converted back to a brown rust (ferric oxide), could I do the same thing as is done when rust bluing and simply boil these barrels until the rust turns black, and then card with 0000 steel wool, dry, then oil? The only difference I could see would be boiling only once rather than multiple times between each rusting pass. If it didn't work out well you could always go to plan B and strip and reblue. I'm sure this wouldn't work out well with barrels that are splotchy or unevenly coated with patina (gun dealers word for rust).
If this would work, it raises the question: since all I have done is reconvert the original finish which turned brown, back to black, does this constitute refinishing? And if it is refinishing, is it less "evil" than stripping, striking, polishing, and repeatedly rusting, boiling, and carding with new rust bluing solutions?