You're basically on the right track. Here's what I do:

1. Using a brass jag, run two or three patches down the bore soaked in a mixture of Shooters Choice and Kroil (75% SC to 25% Kroil). Let this sit for 15 to 30 minutes.
2. Run another wet patch through the bore paying close attention to how much blue is on this patch. If there's an appreciable amount of blue on the patch that means there's excess copper in the barrel. We'll talk about his later.
3. Apply this same solvent mixture to a bronze brush and brush the bore back and forth about 15 or 20 times making sure you completely exit the muzzle before pulling it back through.
4. Run a couple more wet patches through the bore followed by 3 or 4 dry patches.
5. If in step 2 above there was copper detected, then I'll use a copper cleaner such as Barnes CR-10 or Wipeout. Use as directed then use 3 or 4 dry patches to remove this from the barrel.
6. Run a couple oiled patches down the bore and oil the chamber.
7. Before shooting the rifle again run a couple dry patches down the bore to remove excess oil and patch out the chamber also.

I settled on this routine after trying various solvents and methods. After doing this awhile you'll probably develop your own routine. Whatever you decide on, however, I think the following items are important to doing it right:

1. Clean from the chamber end using a bore guide.
2. Use a quality one piece cleaning rod (Bore Tech is my favorite).
3. Use 100% cotton flannel patches, not the synthetic type.
4. Use bronze brushes, NOT stainless steel.
5. Do not use copper solvent with a bronze brush. Use a nylon brush.

Hope this helps, good luck with it.