Re: Copper, and more copper!!!!
Looks to me like you're probably still washing out some old deposits.
If your bore is even slightly rough it will trap copper down in the pores and yep it'll take a few passes to get it to come completely clean. If it's a fairly new rifle with not many rounds through it, then the copper might be getting trapped in machine marks from the rifling process.
Personally I don't believe in lapping a barrel, but I know a lapped (polished) barrel will come a lot cleaner than a barrel with the typical machine marks.
You might need to do several of the soak/scrub/swab passes like you've got pictured there to get it down any cleaner. I usually do two soak/scrub cycles on my barrels after a range session (which is usually 50 rounds at the max).
Actually, that's about all the cleaner that I bother to do my barrels.
There's always a little tinge of blue leftover when I call it quits even after two cleaning cycles.
I use either Sweets7.62 or CR-10 for copper and Kroil for powder/lead fouling.
Just remember to follow the instructions and do NOT let the ammonia cleaners sit in the bore too long or they will start to pit the bore itself.