Elevating the Shogun to Emperor would be an usurpation. From my readings on Japanese history, it would be a non-sense. You could have a figurehead Emperor deprived of any real power, that happened all the time. But the emperor remained a religious symbol, the dynastic continuity was extremely important. I would rather see a government form called Empire but ruled by a Shogun.
Actually all the game is about usurpation, the nightmare of every good aristocrat. Is not only about Japan if we must be precise.
Actually one way to solve situation like this is an expansion about prime ministers, validos, favourites etc... So you have your ruler, but for example you can also elevate advisors or vassals to rule your government, so you can have Olivares in Castille, Buckingam in England, Mazzarino in France etc... and with costitutional monarchies you can Robert Walpole and with the same way you can also put a daimyo as shogun. To have some bonus to stats, diplomatic bonus with a vassal and so on, with maybe a negative hit if the things don't go well during the reign of this prominent character. For example choiche a Valido can improve the aristocrats rebels, and a bad shogun can improve a sengoku jidai in japan against the choosen one, the shogun.
Actually a mechanic like this could be useful for a game of thrones mod too. T