The theory that I have on why the barrel cuts/burns patches may be completely off, but here goes. The barrel and the rifle were made by Charlie Hart (of Hart Custom Barrels) sometime in the early 1980s. The rifle is a massive. It is based on an English sporting rifle with a barrel that is 1.250" across the flats. According to the late Dave Higginbotham of Lone Star Rifles, Charlie built it as his personal rifle for hunting Elk in Colorado. It was made for shooting heavy charges of powder. Recoil for the most part, is not an issue with this rifle. The bore has visible inclusions from its manufacture. When using a tight patch, the bore feels smooth, but just doesn't have the same level of "slickness" as a Green Mountain or other comparable custom barrel. Viewing the bore with a bore light reveals inclusions that run parallel along the top of some of the lands. Some of the worst inclusions are located near the breach.
As mentioned earlier, the first shot from a clean bore will nearly always produce a cut/burned patch, and a flyer. Based on habits developed through competitive shooting, I wipe the bore between shots with a dampened patch. The second and following shots will be on. Recovered patches, with the exception of the first look nearly perfect. A few of the recovered patches on close examination will show some signs of cutting. The weave will look frayed, or burred in some places, but the "cut" doesn't penetrate the patch. My thinking is that the powder fouling softened by the moist patch fills the voids, or inclusions from the rough cut bore. The damp fouling, or just the moisture from the "cleaning patch" also likely helps lubricate the next patched round ball.
The most sensible thing to do would be to experiment with shooting a fouling shot and then wiping the bore with a patch dampened with minks oil, or bore butter, letting the rifle set for the better part of the day and then firing to see if it produces a cut patch and or a flyer.