If Bloodmoon really happend Lycanthropes would no longer exist. If the Shivering isles really happend Jyggalag, now asuming all of Sheogoraths power plus the power he once had, would bring order to the realms of oblivion thus destroying the other Daedric lords.
No, Jyggalag wouldnt get Sheogoraths power because the CoC or the new Sheogorath now has them and it wouldnt be insta-boom power restored. Like I already stated he has no armies of daedra and no plane of Oblivion, where is all the power he would "supposedly" have.
No matter what you say or argue, all DLC and expansions there have been are cannon, this isnt up for debate, this is pure 100% fact. Dont like it? tough. The shivering isles did happen, the CoC did become Sheogorath and jyggalag was freed, no matter what you say, it happened and is cannon lore.