Some rather interesting physics there VF.

Center of mass and center of gravity are the same unless a gravity gradient is involved, like in outer space.

A single projectile that is only as long as it is wide has very poor external ballistics.

None of that is relevant to shotguns at all, as an 'optimum' or otherwise.

The 'square load' is the ballistic equivalent of astrology.



"The price of good shotgunnery is constant practice" - Fred Kimble