Hello Huntsalot:
Welcome Aboard....
It's possible that this might cause your problems.Have you checked everything else like,the scopebase.. if it's loose or not,is the rings tight,,,is the forearm making contact with the barrel when it heats up.Have you tried the o-ring on the forearm screw to free float it,or relieved the wood in the channel to free float it?
I did the o-ring trick on my 308 Suvivor and it seemed to help a-lot...when I shot it enough to heat the barrel up my groups would open up some,also I have had the scope base become loose before and do the same thing.
If you can detect movement or play and it's not the forearm just moving,then I would call H&R and talk to customer service and see about shipping it back to them.You definatly don't want any movement between the barrel and frame.
Mac