I use the Bore Shine. I noticed that after 20 rounds from my 30-06 and 270Win - there is some Cu fouling that shows on the patch, but not affecting the accuracy at that point.
I remember also that my accuracy once got affected after about 150-180 rounds of 7mm RemMag, being only cleaned with Hope's during that time. There were about dozen patches that came blue-green, and I had to apply the solvent several times. So, I will not wait for more than 30-40 rounds to clean - in order to prevent unnecessary buildup.
Before using any Copper solvents, I "wash" the powder residues with Hopes Elite, or any other mild cleaner, in order to come to the metallic build ups. Then, I do the same after the Copper solvent is wiped, so that it "washes" the bore again, from the aggressive solvent. Then, there goes the oil at the end. My bores are like mirror.
Also, another thing that works well on copper is foam (shooter's choice makes it, among others), that is odorless and said to be completely harmless to the bore. I tried that one as well, did the job just fine.