I'm wondering is the problem might not be from something else? I still have some .270 ammo loaded with Hodgden's surplus 4831 and it does not turn my barrels black.
I've also found in cleaning my barrels, that I've never gotten a pure white patch after cleaning.
What you might want to try is some Mpro-7. They may have changed the name to MP-7 now, but either way it's some good stuff. What it is, is strictly a powder solvent that smells like carpet cleaner. It's a bit on the pricey side, but I use it prior to using one of the copper or lead solvents. It seems to clear the way for the metal solvents to work a bit faster.
If the Mpro-7 doesn't work, you might try it with some Chore Boy scouring pad wrapped around a brush. If it works for leading in a barrel, it might work for graphite, if in fact it is graphite.
FWIW, no matter how long you scrub with JB Bore Paste, the patch will always come out black.
It's the nature of the beast.
One more thing about Mpro-7. After you are through using it anddoing what other cleaning chore on the rifle, be very sure to do a proper reoiling of that barrel. Mpro-7 will literally suck all the oil out of the pores of the steel. If you gun has an oil finish, do not get on the stock. You'll never patch it up to look the same.
Paul B.