Howdy
Let's clarify things for a moment.
Are we talking about the carbon rings that build up on the face of the cylinder or are we talking about soot on the side of the cylinder.
Regarding, cleaning the carbon rings off the face of the cylinder, if you are taking days to clean them off, you are spending way too much time doing something that simply does not have to be done. As far as not shooting the gun because you don't want to clean off the rings, that's silly.
The carbon rings that build up on the face of the cylinder are a result of high pressure hot gas blasting carbon and lead particles onto the face of the cylinder.
No, there is nothing wrong with your barrel cylinder gap, this is completely normal with any revolver.
Frankly, I stopped trying to clean the carbon rings off of the face of my revolver cylinders years ago. It is akin to the labors of Sisyphus who is condemned to forever roll a boulder to the top of a mountain only to see it roll down again.
Carbon rings will build up on the surface of any revolver. They are inevitable. They are a waste of time to try to remove. It is a really bad idea to use any abrasive to remove them, because you will inevitably be removing metal too.
Just clean the gun normally. Any rings left on the face of the cylinder, just leave them there. They will not hurt anything, and they will just show up again the next time you shoot it.
I always say, once you have enough revolvers you will realize it is a waste of time trying to remove the carbon rings. You don't have enough revolvers yet.
The other way to avoid carbon rings on the surface of a cylinder is to shoot Black Powder. For some reason, I never get carbon rings deposited on the surface of a cylinder after shooting it with Black Powder. Unfortunately, because of the way Uberti modified the collet at the front of the cylinder on their version of the Schofield, they tend to bind up when fired with Black Powder.