Basically the only thing you would use for a custom is the action and action components. The weight of the Remington action is the same as any other boxlock. Plenty of double rifles have been built on boxlocks, WR being common.
When buidling a rifle you want the majority of the weight in between your hands. manufacturers do this by keeping the barrels thick near the chambers, them quickly tapering the barrels down to .100"-.125" wall thickness at the muzzle. This keeps the handling lively while keeping enough weight to make recoil manageable. All thats left is to build the stock to proportions and dimensions that fit the caliber and shooter.