I will second, "Clean till Gone".
I started using a product called Flitz Bore cleaner on patches first, then on stiff plastic brushes from Iosso and Montana Extreme. As the plastic brush gets worn, you can short-stroke it back and forth in the problem area.
Good Bronze bristle brushes from Pro Shot and Dewey do the heavy lifting when it comes to cleaning, and their best use is in the first 60 cycles of the brush, then put on a new one. Save the used brushes for very badly fouled barrels where you may have to use the worn brush with the Flitz Bore Cleaner, Jb, Montana Extreme Copper Cream, etc. I wash the abrasives out with dripping wet patches of Cigarette lighter fluid till the patches come out clean.
My 257 Weatherbys with short freebore have X Caliber barrels on them, and they are super smooth inside. I am shooting the 115g Bergers/110g Noslers at 3600 so at that speed, I do get a little fouling. I clean the barrel and examine it with a Teslong bore scope usually once a season, which is not much shooting.
These X-caliber barrels are shooting extremely small groups at 500 yards, and I pretty much keep the carbon down to zero build-up with just good brushes. By the time the carbon is going, so is the copper fouling as the copper is easier to remove than the carbon.
It is important to note that Hard cooked on carbon is an absolute bitch to get out, better stay ahead of that job.