Mike,
I have had results similar to yours with Weatherby factory ammo. I bought a bunch of the 100gr Hornady factory loads because I couldn't find brass when I first got my rifle. After initial barrel break-in and getting it sighted in I was getting sub .75" groups. I was at the range with a buddy one afternoon and put about a box and a half thru it without cleaning - I know not a good idea - and my groups kept getting worse and worse, to the point I wouldn't even call them groups. I cleaned the rifle at the range and the results didn't get any better, needless to say I was getting very frustrated. When I cleaned at the range the solvent I used was just a powder solvent, did not remove copper. When I got home that night I broke out the Sweet's 7.62 and gave the barrel a thorough cleaning. Similar to your experience it took multiple rounds of a solvent soaked patch followed by dry patching before the blue patches quit coming. The next time I went to the range I was right back to the sub .75" groups.
I have not reloaded anything for my rifle yet. I had a pronghorn hunt coming up and not enough time to devote to load development, so I decided to stick with the factory stuff.
I was thinking all kinds of terrible things had gone wrong with my rifle before going back to the range and discovering that it would indeed shoot, and that the copper fouling had been the culprit. Given my results, and now yours, I have a sneaking suspicion that Remington had a group of barrels chambered for the .257 Wby that might be a little rough and very prone to fouling.
I think if I were you I would make another trip to the range and see how it shoots post scrubbing before I did anything radical.