hopefully someone with more experience chimes in here, who can confirm that what you're experiencing is actually a carbon ring. (I still think it is, but I could be wrong).
You can try chemicals... get a well known carbon remover, plug the chamber with a plug (sinclair sells plugs for this application), then fill up the chamber (from the muzzle) with solvent... let it sit for a couple of days. Then get in there and hammer it again.
Some guys actually use a reamer to clean up the chamber... It has to be the reamer that cut your chamber (or spec'd the same), and at the very least, you should have reamer stop so you don't cut in too far. This would be "last resort" of course...
When I first ran into a carbon ring (very similar conditions to what you're describing, also in 6BR), it took me a while to get it out. I read on this forum, that this problem is often overlooked, and spinning a brush in the neck (with solvent) every time you clean, is the only way to prevent it from building up to a "stubborn mess". Cleaning procedures are like religion, so not everybody agrees with this. It makes sense to me, and I haven't had any problems since I started scrubbing the chamber neck at each cleaning, so I'm gonna stick with it
Here's a thought... cast the chamber with cerrosafe.
I have never personally done this, so I can't really give any pointers/advice on the process. I also don't know if this would be a good way to determine if you have a big ole carbon ring in there. just search youtube or google for 'cerrosafe,' and you'll see plenty of instructive videos.
definitely keep us posted on what you find/do...