In actual use, where is a gun's pivot point? Is it at the point of balance or somewhere else? Doesn't the actual pivot point depend upon the geometry of the gun in relation to the shooter?
If the MOI is calculated using the gun's balance point and the shooter does not pivot the gun around that point how do the measurements relate to the actual experience of shooting the gun?
Why don't you ask your hero, Barack Hussein Obama, what he uses as pivot and balance points when he is posing with a shotgun for propaganda images in order to advance the gun control agenda you told us he would never attempt?