RE: bore cleaning
Wipe Out is good but DON'T get the stuff on your stock. It will eat the finish very shortly. Don't ask how I know.
The question on my mind is WHY your /06 is such a fouler? Is the bore pitted or what?
If you just have a rough barrel, you might shoot some cast bullets through it. Cast bullets are the best thing that ever happened to rifle barrels. Back not too far they used to "lead lap" barrels to smooth them out. I had an 06 I shot a lot of cast bullets in and the bore got where looking down it was like looking down a piece of chrome pipe. VERY shiney. And the /06 loves cast bullets anyway. It's a win/win proposition.