Mauser06 - no offense taken and thanks for the feedback. I've checked the mounts so I don't think that's the problem. I'm probably going to start first with a good cleaning including a copper solvent. I don't think my solvent (Hoppes #9) addresses the copper issue. Hopefully that will go a long way towards correcting.
At the same time, it's hard to discount the barrel heating correlation. In other words, it seems like this is another part of the problem (even if the barrel is clean) and it would seem there might be a fix for barrel heating (besides sitting and waiting). I would think that this rifle should be able to give me a good 3 shot group assuming I do everything right.
While I am no shooting expert, I do not experience this with my dad's 300 Mag. or .257 (or lighter calibres for that matter).