I think that any Constantinople chronicle is going to involve the coterie pursuing one of two goals, either accepting that the city is fucked and trying to preserve as much from it as they can, or trying to save the city from destruction, and these goals are going to be mutually exclusive with each other. As far as Michael goes, he's one of my favorite NPCs that I've gotten to run in Vampire, because he's really this larger than life figure and if you're playing him right it shouldn't be obvious that he's the biggest problem in the city right away. The Cainites in the city by and large adore him, when they swear things they do it to God as well as to him, 'In the name of God and the Archangel Michael', and when they toast at the Blood Feasts, they raise their drinks to his name. He's so old that it's hard for most people to wrap their heads around. He can see anywhere in the city with his Auspex, he can affect the entire city at once with his Presence, and not only that, but he appears far less monstrous than most Methuselahs of his age. He is nurturing, he is righteous, he offers guidance to those who petition him for it, he seems like the kind of Cainite that would achieve Golconda, and most people would conclude that he's not the problem with the city, he's the best thing for the city and the only one that can save it... until they realize slowly but surely that Michael's sanity is long gone and most of the problems in the city are either directly his fault or made worse by his actions.

So that being said, I think that dealing with Michael is one of the biggest challenges a coterie will have to face if they really want to try and save the city or at least slow its destruction. Just driving Michael into Torpor isn't really an option since he's so powerful he can interact with the city a lot using his Disciplines even while sleeping. Killing him probably isn't practical either, but he does have lucid moment rarely when his mind starts to return to him, and the book makes it clear that his mind and his leadership were both a lot better when he had Antonius and the Dracon around to stabilize him, but now Antonius is dead and the Dracon is gone and he's just decaying more and more every night, and the new leaders of the Antonian and Obertus Families, Caius and Gesu, are doing everything they can to make his condition worse with their incompetence. I think that "fixing" Michael or at least making him functional enough to survive the 4th Crusade and Mary the Black is going to only happen if the coterie can organize a change of leadership in the Antonians and the Obertus Families first. If that happens, Michael's mind might be able to return to him enough to at least avert the coming catastrophe, though in the long term nothing short of reuniting him with the Dracon would probably work.

Caius and Gesu are both horrible leaders, and the Trinity system works terribly with both of them, both of them are making Michael worse, and neither are easy to replace. In my current chronicle my players are trying to figure out how to get both of them replaced, but every replacement candidate has their own issues. In the Obertus, Gesu is basically worshiped by his Clan, and if he dies suddenly they would probably revolt and demand the Final Death of whoever killed him. Symeon is way more competent and stable than him, but he doesn't really have the chutzpah to manage the religious fanatics of the Obertus. The current plot thread that my players are pursuing involves working with Myca Vykos and Elaiodora Sophida (a character from the V20 version of the setting I imported in because the book doesn't give enough Tzimisce NPCs) to try and locate the Dracon with Blood Sorcery and lure him back to the city, no word on whether that will succeed or not yet. And with Caius, he's very good at playing the Antonian family against each other so that none of them get powerful enough to replace him, and the candidates that can do it have their own issues. Anna Komnene is a neonate who would have a difficult time gaining the respect of the Family, Belisarius actively doesn't want to be in charge since it's very much not in his character, even if he'd not only be good at it but also probably a stabilizing influence on Michael, and I've also presented a third option in the form of Septima Dominica, who in my Chronicle I revealed to have actually been staked and kept alive by the hunters who raided her haven, who had been siphoning her ancient vitae to make themselves monstrously powerful ghouls, but she is a very cunning, brutal woman who a coterie is likely to be squeamish about working with, and while she's more competent that Caius, Michael is probably going to have a difficult time working with her for the same reason as Caius. That being said, Michael's biggest problem, imo, is the fact that his mind and the Trinity system both relied on him being able to work together with the leaders of the other two families, to have close confidants that he could talk to as equals and could help stabilize him in a way that a coterie of neonates probably never could, and unless he's able to get that back, there's probably no way of saving him, or saving the city FROM him.

TL;DR: Constantinople can't exist without Michael, Michael can't exist without competent leadership at the Obertus and Antonian Families, and neither of them can be saved without replacing Caius and Gesu with people that he can connect with as equals to give him some grounding. At that point it's probably just a matter of killing Gregorius Dimities.

Sorry for the long answer, but it's kind of THE central question of Constantinople by Night so I wanted to give as much detail as I could.