I have a custom bolt gun chambered in 7mm-08 ackley improved. It has a #2 contour Hart stainless barrel that is crowned at 20" inches. It is very accurate and will shoot like a .280 with a fast burning powder such as Varget. Mine still weighs almost 8 pounds loaded, but it is stocked in a McMillan model 7 style stock and has a standard 700 bdl short action and a Leupold vari x III 3x9x40 on top. Weight is not a real problem as it carries well, but I think for your set up, I would not go with anything larger than a #2. My wife's .280 Rem Mountain rifle has what I believe to be a 1.5 contour, and it shoots 1" out of the box with hand loads.
Hope this helps,
Smoky