Your concept of bore brushes is correct. Just remember to keep them clean, cloth free and they go down the barrel by themselves. Then they won't get stuck. They don't last forever, you will eventually feel them going through easier so they have worn down. Don't be cheap, just get another. Use a good grade of cloth for the bore, not the cheap non cloth patches. Use oil to clean with the bore patches every time except when proving the bore dry before firing. Use rifle oil not motor oil.