RE: Is this normal?
Take a dollar bill and slide it between the stock and the barrel all the way to the receiver to insure the barrel is free floating.
It sounds like a serious bedding problem to me because of the horribly eradic performances between the different loads.......this is not unusual for M-70s to need relief in the barrel channel
IMO there's absolutely nothing wrong about "cheap" core loks....they're a fine deer bullet!!!
You have every right to expect 1.5" groups for five shots and most m-70 will do better than that.