Depending on what the barrel likes, you may be cleaning too much. having some copper in the barrel doesn't mean that accuracy is degraded.
All barrels, especially rough ones, use fouling to season the barrel. This leads to consistency and accuracy.
You will hear of many who will clean their barrels then shoot a few fouling shots before shooting for group. Well, after those fouling shots, they are exactly where they were before cleaning.
I clean only when accuracy degrades. I have found that most factory will easily digest 50rds without any issue. BR barrels can go several hundred.
Try this. With your accurate load, shot groups until accuracy actually degrades. I think you will find that that number is a lot higher then you expected.
The only rifles that have measureably degraded in accuracy quickly were military rifles with dark, pitted bores. Bores worn from thousands of rds and neglect.
I shoot several miliary rifles that still have good rifling. Although the bores are copper in colour, they shoot great. Cleaning them only means I need to shoot 6 to 10 rds to foul them up again.
JB bore lapping compound or bore paste are great at polishing up that barrel. Will help reduce "fouling".
Jerry