You didn't mention if you are wet tumbling, or just washing?
From what I see in that picture, the "carbon" is not all out, so I'm guessing you aren't tumbling with SS media.
Virtually no acid will do more than barely dissolve "pure" carbon. Frankly, virtually no solution period will dissolve "pure" carbon significantly. There's few organic solvents that will touch it. I do dissolution for a living, and C (ash, charcoal, graphite, etc) is the one thing I tell my customers I can't dissolve.
In my experience, the only way to remove carbon efficiently is mechanically. Certain fluids will aid in loosening it, but if you throw a pencil in a liter of any of my favorite acids, the only thing left in a week will be the graphite center (maybe some of the eraser), and the point will still be sharp...
If you're going after carbon, which I agree with, mechanical action (i.e. tumbling or scrubbing) is the only solution...