Below is my general cleaning process.
1) Wet patch bore, let soak 5 min.
2) Wet brush, stroke 10 times (20passes)
3) Push dry patch through
4) Repeat till clean patch
5) Lube barrel as required for storage
The problem I see here is that you are relying on the solvent used in steps 1 and 2 to completely loosen the fouling. In my (comparatively limited) experience, dry patching pushes out loose stuff, but doesn't touch anything adhered to the bore. You end up getting nice clean dry white patches out the muzzle, but there's still carbon and crap attached to the metal in the bore.
My at-range procedure:
Wet patch with carbon solvent of choice, repeat until the patches come out at most a light grey (usually takes 3-5 patches.) Wipe off the muzzle with the last patch (easier to get the stuff off while it's warm.) I'll either take a few strokes with a nylon brush wetted with carbon solvent, or skip straight to copper solvent patches. Wet copper solvent patches with a few minutes between to allow it to work. Dry patch, dry mop the chamber, and resume shooting or pack up to go home.
At home, I'll use the Teslong to take a look and see if there was anything I missed in the bore, and check for carbon buildup just ahead of the chamber. Action taken depends on what's found: Iosso on a VFG felt pellet spun (by hand) to remove carbon ring, more copper solvent, a couple of passes with a bronze brush for carbon in groove corners, etc. Every now and then (probably 200, 250 rds or more) I'll do a full length cleaning with Iosso on either some VFG pellets or a large patch wrapped around a Parker-Hale jag.
I generally use the Boretech products (CU2+ for copper, C4 for copper), but have been trying KG-12 for stubborn copper recently. Still on the fence about it. If I miss some carbon on the muzzle (I use a VAIS brake which seems to bake carbon on the muzzle, but remove the brake for cleaning), CLR will usually get it off without too much trouble, assuming the C4 doesn't.