IMO the best investment you can make right now is either a bore scope, or an endoscope with a 1 to 2 centimeter focal distance. The endoscope will allow you to see the whole chamber, neck and leade to identify trouble areas and confirm your cleaning process, whereas the bore scope gives a more "soda straw" view, a very close look at a small area.
Both have their uses and strong points however, I prefer the broader view so I use the endoscope which I also use to look in the muzzle end and plainly see copper build up where it is more likely to occur.
With that in mind, to clean out carbon rings I put a bronze brush on a section of 3 piece cleaning rod, chuck it in a cordless drill and spin the brush in the neck/lead, then confirm with the camera.
There are many inexpensive endoscope cameras available, some that will bluetooth to your phone or PC (I just bought this one
https://www.amazon.com/dp/B01MYTHWK4/?tag=accuratescom-20 ), but not many with a focal distance close enough, so choose wisely. NOTE: the one I just bought has a 5 cm minimum focal distance, which is too far for good viewing in a chamber.
I've been using a Snap-On BK5500 like this one
https://www.ebay.com/p/Snap-on-BK5500-Visual-Inspection-Scope-Camera-Device/1011864405 for many years with good success.