To me (I'm not an expert), it sounds like the barrel's bore has some rough surfaces and pitting that are catching the copper jacket and stripping layers off of parts of the bullet. This "stripping" action is uneven and results in a bullet with a damaged center of gravity. This could lead to unexpected excess spin drift. I've seen this problem happen at barrel-burner speeds like 2900-3000fps, but disappear at lower speeds. It's also possible that the throat has a pretty gnarly burr on one of the lands from potentially sloppy chambering.
If you've cleaned your barrel with a good bore cleaner like Montana Extreme 50BMG, Boretech Eliminator, or Sweets 7.62, and that didn't help, then check the muzzle end with a caliper to find the groove/bore diameter. If the bore diameter (on the lands) is between 0.298 and 0.301, then you're good. The groove diameter should be somewhere between 0.307 and 0.309. These are pretty wide ranges, but they're guidelines a wise old man once taught me.
If all else fails, try wrapping a slightly undersized (7mm) stiff nylon brush with a bunch of patches and coating it in JB, Iosso, or Flitz. Run that up and down the barrel (not out the muzzle though) until you feel like the barrel has been adequately polished. If that doesn't work, then you really do have a bad barrel that needs replacement.
The good news is that you can now get Remage barrels for not much more than a normal barrel blank. They use a savage-style nut so you can swap your barrel at home. I think Criterion makes them.
My $0.02[/QUO
I had the same problem with the stock barrel. Got no accuracy after 2400 fps. A friend checked the throat & sure enough it was bad. Not the first one I've heard of in Rem 700. Switched to Criterion Remage & never looked back. I shoot 1000 yard silhouette with moa targets. No problems since.
BW