I use all the things that apparently i shouldnt, but then again my barrels are not under warranty or anything like that.
And surprisingly, they all look great in my borescope, and all still shoot!
I still use CLR - nothing in my shelf gets carbon out quicker. Blue iosso brush with wrapped patch, wet with CLR, spin in the throat followed by 15-20 short then long strokes and carbon is gonzo. Fast. A good rinse with alcohol and a wet patch of Kroil, then a few dry patches, and the barrel is squeaky clean.
If i want a mirror finish, a patch/jag with Iosso and Kroil does it everytime.