You may be under a misconception, the natural stance with a shotgun is with it at diagonal to your shoulders.
I agree that my form is not the "traditional" stance (back foot pointed at a 90 degree angle, body bladed to the target):
However, the "combat" stance that the Marines have been teaching me squares us to the target (both feet pointed forward, which enhances mobility; body turned towards the target to take advantage of our body armor):
This is the stance that I've been trained on and what I'd like to continue to use. In such a case, the shorter LOP is essential for a smaller guy like myself.
A helpful video
(got it from somewhere on these forums while researching/rooting around).
Thanks for the clarification.