Carbon is the hardest thing to get out of the bore, the old method for removing carbon and corrosive salts was poring boiling water down the bore. After getting the carbon out if the bore doesn't come clean after two applications of foam bore cleaner then your bore is a sewer pipe and even if you could get it perfectly clean the next time you pull the trigger your right back where you started.
Below a badly frosted and pitted milsurp bore.
Below a hand lapped custom rifle bore.
Below, before and after fire lapping a brand new Savage button rifled barrel.
Below, the shocker, magnified closeup of a new button rifled barrel.
The throat
Two inches from the muzzle
I use foam bore cleaner and use a cleaning rod a little as possible, as you can see above a barrel can and will "EAT" a copper bore brush and give a false copper reading from eating your brush. If you do not have a custom barrel then just give it at max two applications of foam bore cleaner and stop. The bore will be a copper magnet as soon as you pull the trigger again anyway.
More rifle barrels are damaged from cleaning than for any other reason, and foam bore cleaner doesn't have any sharp edges.
Let the foam do all the work, below a 1943 Enfield with a frosted bore and one shot of foam bore cleaner.
If you don't see any blue coming out of your bore after using foam bore cleaner then chances are what you are seeing is a carbon buildup.
"Remove the Carbon First, then Attack the Copper
Here is what we recommend for an “average” factory barrel. After 25 rounds, or when accuracy degrades noticeably, spray some MPro7 or GM Top Engine Cleaner (TEC) down the bore from the muzzle. (Insert bore guide in breech first. Keep your MPro7 or TEC in a small plastic pump bottle for muzzle application). Let that sit a bit, then follow with a patched soaked with the same cleaner. Repeat. SharpShoot-R Carb-Out and Slip2000 Carbon Killer work really well also, when applied with soaking wet patches. Then, apply the same MPro7, TEC, Carb-Out, or Slip2000 generously to a bore brush, and run the brush through the bore 3-4 times, breech to muzzle."
Bore Cleaning Methods and Materials
http://www.accurateshooter.com/technical-articles/bore-cleaning-methods-and-materials/
I use GM Top Engine Cleaner (TEC) and boiling water to remove the hard carbon buildup. The hot water causes expansion and contraction of the bore and breaks up the carbon.
And again, boiling water and foam cleaners cause no wear or damage to your bore.