Ditch the kroil, purchase Free All with the spray attachment on the can, 14 oz. Free All has a chemical that will actually dissolve carbon, but it takes time.
Free All will shock the heck out of you on getting old rusted bolts off a front ends, or rusted on bolts on a tractor/horse trailer.
fedpro.com
Use the arrow and drop down to the 14 oz pump sprayer
Very inexpensive postage from the company.
Free All works to work through the carbon, and the carbon is in layers. Nothing beats a high quality bronze bristle brush, with a max of 100 strokes on it, 60 strokes does a better job.
If carbon persists, then to to an Iosso or Montana extreme plastic brush, brush with one of several products, JB, Montana Extreme Copper Cream, or Flitz rifle bore cleaner.
Different calibers, different powders, shot strings, Barrel quality, barrel erosion, frequency in-between cleanings, will all demand a very different approach in each.
The approach of one method fixes all is very incorrect thinking. A bore scope will give you a PHD in gun cleaning, but ignorance is Bliss....till it is not.