The best way I've found to inside clean case necks is to use a brass bore brush mounted in an electric drill and simply run it in and out of the case until you see a nice clean surface in there. It really doesn't take long to do and will allow you to make more uniform reloads and not damage the brass.
I shoot mostly pistol ammo now with my powder coated cast bullets. I don't have to clean case necks as the case polishing process I use now gets the inside of the cases looking like they have never been fired yet. What I do now is use small ceramic pellets as the cleaning media and use a solution of water, citric acid and dawn dish detergent to clean the brass. I just put enough pellets in the vibrator case cleaner to cover up the brass and let it run about 2 hours. Then I sift out the pellets to be used over and over again. I rinse and dry the brass and it looks like brand new brass inside and out and don't have to worry about carbon in the necks.
About 8 or 10 years ago I was competing in a varminter type match where you shot from 200 to 600 yards at berms that were at 100 yard intervals. I was shooting a 6 Ackley with Tubbs bullets. These bullets were lead but were wearing copper condoms. I could shoot 6 inch groups at 600 yards with brass loaded with carbon in the necks prone with a bi pod.
Since I suspected that my vertical dispersion was being effected by different amounts of friction in the necks I made a gauge to measure neck pull in each case. My goal was to sort out or match up all my cases so that they had the same amount of friction on the bullet as it left the cast during firing. The gage was built sing a B Square arbor press where I mounted a 6mm dia. polished stud that could be inserted into the case necks to the same distance each time and then measure the force needed to pull the stud out of the neck. This allowed me to measure the neck pull and sort out the brass by neck pull tension. All cases had necks turned to .012" thickness but had different numbers of firings on them and different amounts of carbon built up in the necks.
My testing showed that, on my scale, some cases measured as low as 20 and some as high as 80 or 100 to extract the stud from the neck. I.O.W. big differences in neck pull between the cases I was using. Seeing this, I decided to not try to match up them for batches of the same tension but to bring all the cases back to the same condition on the inside of the necks prior to reloading them. I did this by cleaning all the necks each loading cycle back to a clean surface which was the most consistent condition I could achieve.
It worked!! My verticals at 600 yards went from 6 inches to 4 inches. I also matched up all the cases to the same neck pull for the 500 yard and 600 yard stages of the course.
One thing that I learned from measuring neck pull was that carbon in the necks increased the friction required to pull the bullet out by, on average, doubling the force necessary to pull it out under a static condition. If the mean force for clean necks was say, 40, it would take 80 units of force to pull the same polished .244" dia stud out of a carbon fouled neck.
In summary, you can probably fix your problem by cleaning each case neck by abrading the carbon off using a brass brush or you can do it in the case cleaning process by using some sort of media that will abrade it off the necks that way.
The media I'm using was given to me by one of my sons who was working for a company that built shot peening and de burring machines for the industry. The little ceramic pellets are in two shapes. Some are round and about .200" in diameter and the others are in the shape of a cylinder about .300" long and .075" in diameter. These have the ends cut off at a slant to provide a sharp end to abrade the material they are being used on. Neither one seems to cause any problems with bridging inside the cases except for maybe one in 500. So, I do have to check each one before sizing them just to be sure they are clear inside. Other shooters that I know use small steel pins that are available through normal suppliers for reloading equipment. They seem to work just as well as the ceramic media my son provided. One advantage of using steel pins is that they can be easily collected by using a magnet and never wear out.
Your mileage may vary.