At the risk of having to hear the howls of disagreement, here goes...cleaning carbon out of barrels,whether out of the bore/throat area,or out of the case neck area(2 different locations), is difficult at best. The carbon is layed down under high pressure/ temperature/time,and will not come out easily. It's going to take elbow grease,and it's going to come out in layers. The Carb-out works on fresh carbon,but not by patch alone in my experience. You need to use a bronze brush along with whatever "super sauce" you're using. The best/fastest carbon remover I have found to date is RB-17,with a bronze brush. The RB-17 has a gel like consistency,and will stay on your brush/bore. Having tried numerous iterations of methods I've learned there is no magic bullet. Now,IMHO, if a bronze brush was detrimental to the bore,so would a bullet be traveling down the bore,wiping the carbon and powder fouling along with it.
Having said that,that is why the carbon is so difficult to remove. In a long abused bore,it will take much time and elbow grease to clean. I believe that what happens is the various cleaners oxidize the surface of the already hard carbon,and that is why your cleaner will no longer show "color". I have a Hawkeye and a Teslong to back up my findings. I prefer the Teslong as you don't have to be hunched over the rifle for long periods,and you can take pictures easily. We are entering a new era by having borescope to really see how our cleaning methods work. I have not documented all of my results to show everyone,but plan to do so on the next "ugly" bore that comes in.