Please do not use the JB red paste....ask
@Frank Green of Bartlein barrels.
As for how to use a mild abrasive like JB Compound (blue), I also follow Mr. Green's advise and its worked well for me.
I've used the JB blue and Rem 40X which is even more mild. I don't use abrasives often but have done so...mostly when I see carbon building up just past where the case neck ends.
Get a Parker Hale style jag (the ones you wrap a patch around like rolling a cigarette), rub some paste into a patch (I dampen it first with Kroil oil...just makes it a bit easier to handle), wrap the patch around the PH jag and run it back and forth 10-15 times without exiting the muzzle, and then short stroke up by the throat.
If all you are interested in is that carbon just past where the neck of the cartridge ends, just do the short stoke. You will have to back your bore guide up a bit after getting the jag/patch into the bore so as to get to that area.
And one other thing you said that caught my attention...."It made the whole barrel spotless and immaculate". Just my view but you aren't doing yourself any favors by always scrubbing it to bare metal.
Best of luck