Try to find some "Scotch-Brit" or "Scotch Bright" pads at a hardware or perhaps wood finishing store. They are coloured as to how coarse they are. I think the green is too fine and would use the red colour.

They are a woven plastic-sort-of abrasive pad- about 1/4" thick and 10" square.

Cut about a 1 1/2" square and put that over a jag - with some form of thin lubricant, like WD40/Varsol/Kerosene etc. Scrub the bore with that.

This is what we advise fellows with brand new Muzzleloading barrels that are cut rifled and have sharp edges to the rifling that is cutting the patches. This coarse 'cloth' will smooth the edges without damaging the bore.

It might help your gun.

Ned Robert's Book, "The Muzzle Loading Cap Lock Rifle" written about 1934 or so, explained lead lapping fairly well.
:in a nut shell:

A tapered "Lap" is turned, that has about 1" long threaded male end and a threaded female end. The diameter is not important, but large enough that you do not need 5 pounds of lead to cast the lap on it.

The female threaded end is screwed onto a substantial rod. A washer of some sort to plug the bore at the rod is needed. The rod is inserted into the bore to the muzzle- usually, with only a small amount of threads sticking out.

USE ONLY PURE or DEAD SOFT LEAD

Lead is poured around the tapered lap plug until it comes out onto the threads about 1/2". After it cools completely, the lap is pushed out the bore AND a nut if run onto the threads up against the lead.

Lube the lead and push it through the bore one end to the other making sure it will fit. It is then removed and rolled in fine valve grinding compound - lubed with light oil and reinserted into the bore. It is run up and down the bore, breech to muzzle, back and forth, back and forth until it gets 'sloppy'. Then the nut is tightened to expand the lap and again it is run inside the bore.

Repeat:

After many hours of this, you may have to cast another lap and start over. What fun!