I've sold a couple hundred Model 70s over the past decade, and own a half-dozen of the Classics myself.
The biggest problem I've seen with the newer Model 70s is uneven or inconsistent forend pressure. The cure for this is to free-float the barrel.
I had a customer who bought a beautiful .264 Win Mag Classic Super Grade with an incredible crotch walnut factory stock. The rifle wouldn't shoot inside 2" and he was very upset. I took the rifle in for evaluation and shot it, and noticed that it shot much better groups when the sandbag support was under the action than when it was under the forend. The rifle stock was touching the barrel, and any forend pressure made it flex and touch the barrel even more. We opened the barrel channel up sufficiently to be able to slide a dollar bill up to the action, then cut a small groove in the barrel channel from the forend tip to within an inch of the recoil lug, and then filled that groove with Acraglas to stiffen the stock so it wouldn't flex. After that, the rifle would consistently shoot under 1 MOA with factory ammo regardless of where the forend was rested, and the customer was very happy.
I've seen this with several USRAC Model 70 hunting rifles, and so I wrote the factory about it, and suggested they open up their barrel channels slightly to ensure the barrel is free floated from the factory. USRAC believes that customers want a nice, tight stock-to-barrel fit and see it as a sign of quality. They don't realize that they are giving up the accuracy mantle to the Remington 700 unnecessarily (my Model 70s all shoot under 1 MOA as long as things are as they should be, i.e., free floated barrel). I guess it would take a little effort to modify the CNC program that routs the stock out and no one seems willing to do this.
Check your barrel to ensure it's free floating. Check it again while resting the very tip of the forend on something and supporting the rifle only via the forend tip and the very end of the buttstock (to ensure the maximum reasonable pressure is exerted on the forend to make it flex). If you can't easily slide a dollar bill up to the action and back, it's too tight.