The heaviest fouling will be at the breech end of the bore.
There are many ways to polish and smooth a bore. Here is a
@duelist1954 video showing the process he used on a difficult to load GPR.
I have used a similar method with Scotch-Brite for some time on all my new or new to me barrels, and Mike explains his very well. I started doing it after speaking to Don Getz (Getz Barrel) years ago before he passed, and he recommended using the green (600 grit) Scotch-Brite for smoothing up barrels that were cutting patches. Said it wouldn’t hurt the barrel.