I had a blued/wooden version of the Remington mountain rifle in 243. I found two things out about these rifles, and the same can be said about the Remington Model Seven.
First: They both have tapered, skinny fore ends. This made it just a little bit harder for me to hold it still at the bench.
Second: I was treating a pencil barrel the same as the regular heavier barrels. That was my mistake. I later learned that if I just shot two rounds and then put the gun away until it was completely cold again, I could repeat the same group. I'm talking an inch or under with regular factory ammo. That was the trick for me. I miss that rifle, but I still use my Model Seven SS in 308 all the time and boy is it accurate, if you just let it cool down!!
My cousin owns a Laminated Stainless Mountain Rifle in a 30-06. He says it is probably his most accurate rifle. But he also learned not to let it heat up.