OK. Here is my penny worth of thoughts.

First of all, according to NASA ( http://www.grc.nasa.gov/WWW/K-12/airplane/cg.html )
”The center of gravity is a geometric property of any object. The center of gravity is the average location of the weight of an object.” Thus all the CG is a center of the mass of the object. This is mechanics, at best kinematics, not aerodynamics.
Stall, AOA, etc. IS an aerodynamics. The relationship – zero to none! The relationship is only in the amount of energy (I am using mechanical term on purpose) the engine produces TO COMPENSATE ALL OTHER forces, including gravitational force, the weight, so the plane can fly.

Technically, even “perfectly balanced” plane will eventually stall when the speed is low so wings will not be able to “hold” the plane in the air anymore. With CG moved forward or aft, left or right you just adding another variable to the equation. All you do is shifting weight, thus creating an additional force which causes the plane to go towards CG, and all it does is TRYING TO FIND THE POSITION at which it will be perfectly balanced again (kinematics)!!! Unfortunately, with all these MECHANICAL changes you are inevitably affecting planes AERODYNAMICS by shifting AOE, thus you causing stalls at higher speeds, but again, because you are changing aerodynamics of the “wing against wind” condition, and not because you have shifted CG.