I'd like to thank everyone for the helpful advice, and address the following comments:
Jhalcott asked:
WHY are you scrubbing the bore with that abrasive stuff???
And Riciardelli stated:
Secondly, I don't believe in ever running anything down a bore which is abrasive. And I believe that most barrel makers agree with me.
I'm using the Tubb Final Finish bore polishing system. It ain't like pouring sand down your barrel. It is a set of 50 bullets; 10 each in 5 successively finer grits. The grits are very fine. They do not feel gritty or abrasive to the touch. After having used it in one previous rifle, I'm a believer. If I bought an expensive, after-market barrel I doubt I'd bother with it. But with an inexpensive, factory barrel I feel it does more good than bad. I'm not telling anyone else they should do the same, but I like it.
One other thing: if you buy a fancy, hand-lapped barrel, do you know what's in those lapping compounds they use? Answer - ABRASIVES! When they polish a lacquered finish on an expensive table top, do you know what they use? Answer - ABRASIVES! When you brush your teeth, guess what's in the toothpaste that cleans the crud off your enamel. Answer - ABRASIVES.