I've had good luck with Gunslick foaming cleaner. I'd imagine it's close to the Outers you got @ WalMart. I may have to do 4 or even 5 treatments, letting it soak (with cotton plugging up each end of the pipe) for 2 hours or up to overnite. But I don't have to scrub!
I've used Shooter's Choice ammonia stuff, & it works, but I worry about leaving it in too long, & it still takes multiple treatments.
The bore on my .30-'06 CDL picks up a stupid amount of copper, but it can shoots some awfully pretty groups, so I put up with it.
Let us know how the foam works for ya.
FC