Wipe-Out. Jag/patch only.
The only consensus, that everyone should agree on, is to use a bore guide- and a quality, one-piece ball-bearing rod.
Throw away those two or three piece Hoppes cheap aluminum rods. They will flex and scratch the inside of the bore.
A good bore guide will keep the rod centered and prevent it from sliding along the rifling- in addition to protecting the chamber area.
If you choose to use nylon or bronze brushes, they say not to run them back through the bore, as reversing them will scratch the crown. Now, I don't use brushes- just jags/patches and Wipe-Out as mentioned above. But, I never have figured out how a brush could be "safe" to run down the bore, but could scratch the crown...
I use a dewey coating clearning rod which I've always thouht were very good. Ball Bearing?
So you don't run a brush at all? Are you able to get all copper fouling out with just jags and patches? Have you not cleaned your rifle for a week or two after shooting and are still able to get all of the carbon out?