The barrels are quite heavy relative to the stock and, especially, the action. 4 to 6 oz added at the butt plate of this gun would probably bring the balance point to your prefered 4 1/2" and would move the MOI up even more. Yet, the gun would then barely break 5 1/4 pounds.

An interesting gun for someone wanting to shoot a .410 SXS on a budget and/or with a modern gun.