I really don't go for perfectly clean. Your gun is going to copper back up in a few shots anyway so once I get most of the carbon out and there's not much blue on my patches I call it good.
I do this too although I don't try to remove the copper unless it's heavily fouled and I've not found that happen with a good barrel. I usually run a patch with automotive carbon remover down the barrel and let it sit for a few minutes. Run another and then some dry patches. The borescope shows no carbon. I don't see the reason to remove all the copper only to deposit more when shooting.
I used JB and Kroil on my factory 264 barrel religiously. I haven't used it on custom barrels.