Stop with that logic already. You're doing it wrong.
Gods are not persons. They are concepts, they are their sphere, they are their realms, and the lesser Daedra in that divine trinity sense.
To become Sheogorath you must symbolically become him, his staff, his clothes his powers, his appearance. You become Sheogorath, by being Sheogorath.
In otherwords, Sheogorath doesn't change but the Champion of the Isles does.
I know that is what rightfully should happen, I just figured that since they already broke that logic (understandably) in SI, then it would most likely not carry over.
They'll handle it by not changing a thing because they don't have too. Why would they even pose this question to themselves? I think its a pointless question.
How do you think they would handle it? Or rather, how should they handle it?
The answer is simple. He is most likely going to keep the same form. I don't see any other way around it.
I know he will most likely keep the same form, but I think the devs put themselves in a [censored] situation with this one. I just posed the question to point out that there needs to be a break in logic somewhere along those lines, and in the hopes that someone had a better answer for me than the obvious.