See if you can borrow a retired Drill Instructor from Parris Island. Maybe a Guy like Gunny. Have him stand in back of you while you clean. It'll solve all your problems and it won't matter what solvent you are using.
Just Kidding
Send the barrel to Bobby Hoyt and go watch The Big Sky for a while. It'll come back looking like a mirror inside but you may need bigger bullets next time.
Just Kidding
Tell the missus you'll do the dishes if she cleans the barrel. It's easier doing dishes.
Just kidding
At the end of day two at Dixons Rifle Fair I still had a twenty in my pocket. So I wandered by the tent that housed The Chambers crew, resisted the urge to buy a stock blank from the guy next to them because I am simply not talented enough, turned away and....Lo!!! The Lord spoke to me and by divine hand placed this guy with a little brass and rubber unit that clamps onto the breech by the touch hole right in my path. I brought it home, put a hole punch to the cap of a Deer Park water bottle, pulled the brass end, slid that onto the hose, replaced the brass end and loaded up the bottle less than half way with hot water. The end of his little device went into the bottle and the clamp onto the barrel.
Maybe twenty vigorous pumps or so, possibly with definite Freudian implications, and that barrel came out spotless. I didn't take prisoners. Spoke to it lovingly and dried it thoroughly, WD40'd it and then lubed it with somebody's oil.
Slap my face and call me Heretical, but that little tube was so effective I used the same file to round the breech face where the heat vent meets it to cut a small groove above the side plate to house the clamp when I make a gun. Not being a devotee of historical school accuracy, now when I go out with my sons or grandsons we are done cleaning in time for pasta and sauce.
You might want to yank the breech plug, get rid of all the black stuff that the guys in front of me in this post advised you to get rid of, and find this little tube thinggy.
I'm not kidding
Don't shoot yore eye out, kid
The Capgun Kid