IMO you are more likely to have carbon and wad plastic fouling than lead. There is a reason wad cups are...well, cups.
As far as cleaning barrels, I personally use a brass rod chucked into a drill and threaded on one end to accept a bronze brush. Birchwood Casey Bore Scrubber down the bore, brush in rod chucked into drill, then go to town. Patch out afterward.
The Bore Shine is, IMO, more of a wetting agent to keep stuff in suspension so it can be patched out more than a solvent. Mechanical agitation is your friend.
If you don't have a brass rod then I suggest tornado brushes on a manual cleaning rod with Bore Scrubber. Then patch out.
Cheers