First is the assumption that Sheo and Jyg are opposites, indeed that madness and order are mutually exclusive. But they are not. A very common mental disorder here in the real world is Obsessive Compulsive Disorder, which can be very severe to the point of as disabilitating as any other form of madness. And OCD is the desire for everything in life to be perfectly ordered. Trying to order an imperfect world is just as insane, if not more so than babbling on about cheese. Thus Sheo and Jyg are not opposites.
The second is the fact that we are believing the Daedra of madness that he is not insane. The most dangerous maniacs in history have been the ones that believe that they are sane. Charles Manson, a man that most of the world believe is a complete psychopath, still insists that he is completely sane, and that his delusions are the truth. But the minute the Prince of Madness says he is not insane, we believe him, thinking he is cured.
The whole concept of Jygallag is fundementally insane as well. Jyggalyg's primary purpose is to strive for complete order. But his very existance is as a being that was born through the conflict and instability of Anu and Padomay makes his very existance contrary to his own purpose. For complete order to exist, only Anu may exist, and the existance of Jyg is proof that complete order is impossible in this universe. And his belief that he can order it is just a delusion on a grand scale.
Thus I will go on a limb and propose a theory that says that Jyg is just another figment of Sheo's fevered mind. The Greymarch is as we know an act of self-destruction, which is an act of insanity. Jyg's goal for perfect order can easily be seen as insane, even lining up with a known mental illness. And his feelings of grandeur and him self-defeated purpose are delusions to a grand scale. Who is to say that Jyg is not just another personaliy of Sheo that believes he is seperate. And that would make the PC just another mortal svcked up into the Prince's madness, and lines the PC more with Arden Sul.