I think what you're looking for is a forearm rework that was developed about ten years ago and popularized by writer Ross Seyfried.
I don't know where you'd get particulars on this, but essentially the work consists of having a metal plate glass bedded inside the forearm with a "tension screw" through the middle that presses against the barrel. You simply experiment with different settings on the screw until you find what works on your rifle.
In effect you are not only applying tension to the barrel, but glass bedding the springs, etc, in a way that they no longer bind with the barrel as it heats up.
I had this done on a 7mm Mauser #1 several years ago and it worked like a charm. The rifle was still no tack driver (though I never really experimented with "accuracy loads" - this was a deer buster), but the forearm work cost about $100 bucks and shrank groups from 3 - 3 1/2" down to about 1 1/2" with my heavy hunting loads. It works.
I'm sure somebody in the gunsmith forum could give you better info on this technique.