One hole in the theory comes into mind: Zangetsu doesn't necessarily mean "Moon cutter." It can also mean "Cutting Moon" (which makes more sense IMHO, based on the shape of the blade and on its attacks). Notice that Suigetsu is translated into "Water moon", why can't Zangetsu be translated into "Cutting/beheading/killing moon"?
So, it can imply the theory, or the opposite, that Ichigo's sword is somehow similar to Aizen's, like how there may be different "Moon"/"Getsu" swords scattered all over the place, and Aizen is only the first. Hard to see Kubo create a villain that trumps Aizen, though.