I’m my limited experience (a total of 2 complete take downs of the Model 12), this is the only way to correctly remove the barrel from the extension without marring it up. I’m sure there’s other ways. I don’t know what those ways are. An old timer suggested putting the barrel in a lead lined vise, wrapping the extension with leather and using a big pipe wrench or 15” crescent to turn it. I didn’t want to try it that way.
Those barrels are screwed in so damn tight to that extension sometimes it’s a pita even when using the proper tools. If I ever re-do another model 12 anytime soon…I’ll just leave the extension and barrel coupled together while polishing.