But does his Sheogorath personality go dormant within him, or is his madness completely lost and then regained?
At that point, I'd say merely dormant. In the end when Jyg normally does take the throne, he'd have defeated it all.
At that point he'd turn into Sheogorath again either because of the curse (lame) or because the unpredictability of Mundus drives Jyg insane - or said otherwise the creation of Mundus prevents the concept of predictability to exist fully in the Aurbis.