Carbon ring forms between the mouth of your case and end of the chamber where leade begins. A year or so ago on another site, someone suggested this method for removing the carbon ring: Get an old arrow, remove the tip and thread your brush in, one size smaller than bore diameter. Wind patch around brush, smear JB all over the patch. Remove nock, place that end of arrow in a cordless drill. You don't need to use bore guide, but keep the brush running straight for about 30 seconds in the carbon ring area. I have used this method, but without a borescope, I cannot be certain of its effectiveness. Lately, I am using GM top cleaner mixed with Miracle Oil 3 to 1 ratio. Its OK, still takes elbow grease.
Tried the NECO method of fire lapping several years ago on a .22-250, but did not feel it was effective. What are the consequences of just degreasing your favorite bullets, then smear several grades of gritty paste on them and firing? Cleaning after every shot or so, of course.