I tried kroil and JB . some carbon came off but hard carbon will not move. maybe more brushing.
I'm wondering where in the barrel you are seeing "hard carbon" and (not intending to be rude) if you know what you are looking at. Can you post up some bore scope photos of the "hard carbon"?
I have never heard a differentiation between carbon build up and "hard" carbon build up. Is it smooth or checked looking like dried mud?