You can also use Flitz. It is a little bit more aggressive than JB but is still a polish and will not remove any detectable amount of steel from the barrel.
I use Flitz to polish the inside of steel reloading dies.
Cleaning, we don't use Pyrodex, only BP. My kids were competing with muzzleloaders and when shooting/cleaning 3 or 4 times a week, they really got a routine down pat.
- Pail of boiling water, added some of their patch mix, (Pinesol, water soluble cutting oil, ethyl or isopropyl (rubbing) alcohol),
- remove nipple,
- run a soaking patch though to get really dirty stuff out
- stick breach end in bucket,
- clean outside of barrel and other parts in still clean water
- use tight patch and it acts like a piston drawing water up barrel and scrubs it at the same time.
- finish with coat of bore butter
If we were using Pyrodex, then we would be using Break Free or CLP, because part of the Mil specification is that it neutralizes chlorates.