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Silence is Acceptance. "To stand in silence when they should be protesting makes cowards out of men." ~ Abraham Lincoln ~ Stand Up and Be Counted !
I'm a benchrest long range competitor and get a chance to see alot of guys in action cleaning just about everything made on the planet and the one product that I see used only when alot of fouling is showing is called "TM"..and also "GM" top engine cleaner..... now remember these are not standard of the shelf barrels and most of these guys baby them beyond anything that a hunting barrel would ever see in a lifetime, I can tell you that "TM" is awesome but make sure you wear gloves, it will remove your top layer of skin also....
I use wipe-out followed by Butch's for general cleaning. Every 2-3 cleanings I'll plug the barrel and soak it in Barnes CR-10 for 20 minutes, it strips copper very well. But wear gloves and keep it out of your action, it's not mild stuff.