Brushing will help and will NOT harm the ultra-hard chrome lined bore.
You're doing it right, which is to allow the bore solvent time to work.
It just takes soak time to get all the copper fouling out.
I'm anal-retentive about cleaning my guns, and I allow soak time followed by running a clean soaked patch through the bore in one smooth pass.
When it comes out, I look for green or blue stains. I continue allowing the solvent to work for another 30 minutes or even longer until a patch comes out without stains.
"Pumping" patches up and down the bore serves no useful purpose.
Also, if you're shooting military surplus 5.45x39 be SURE you flush the rifle with HOT water to dissolve and flush out the corrosive salts. ALL current surplus 5.45 is corrosive, no matter what one or two importers have said.
Keep at it.