Personally I like the theory that the CoC didn't become Sheggorath, but instead went insane inside the Isles (Basically most of the adventures in the Isles were delusions).
To me, at least, it makes more sense. No mortal is beyond the mental stretchings of Sheggorath, and IIRC it's never been explicitly stated "The CoC became Sheggorath", only, perhaps, loosely implied,
How is it loosely implied when everyone calls you Sheogorath at the end? When your madness is so great you can speak with mad beggars, who thank their lord, Sheogorath, that is you, for being able to understand them?
Also, the narrative itself never supports the idea that the CoC was simply delusional, and in fact, arguing he was delusional ruins the point of the expansion and it's story.