First, bronze bristle brushes do not harm the bores of rifles. Benchrest shooter for years have used them with their expensive barrels. I use them exclusively in my expensive barrels with never a problem.
For cleaning the fowling out of my barrel, I use a 50-50 mix of Kroil and Shooters Choice, but any good slovent mixed with Kroil works.
For copper fowling, I use Sweets, and leave it in the bore no longer than 20 minutes. There are other copper removers on the market that are very good too. I just have two bottles of Sweets, so I use it rather than trying someting "better".
That is my regimen, and I have bright shiney bores when cleaned this way.
I started centerfire benchrest shooting in 1970, and have developed my procedure based on cleaning those very good barrels.
For barrels that are not lapped by the barrels maker, as expensive aftermarket barrels are lapped, I polish the bores with JB Bore Cleaning Compound; for factory barrels that come un-lapped. I use a tight fitting patch loaded with the JB Bore Cleaner and run that through the bore 100 strokes. JB has an emulsified fine abrasive in it that will not harm a barrel that needs lapping. I'm just doing what the expensive aftermarket barrel makers do, polishing the bore. The barrels come out bright and smooth inside after the JB job. Doing this improves my accuracy, and makes cleaning a breeze. And, I don't get the copper fowling that I did before doing the JB job.
US Army Retired
NRA Benefactor Life Member