In my opinion, I don't think it would form a fifth madhab since Sirozi doesn't really care about changing how Muslims should interpret Sharia law but more about how people should live their lives under Islam. If anything, he might just follow the Hanbali school since he's influenced by Ibn Tamiyyah and he's essentially an earlier counterpart to al-Wahhab.All correct except for the name--I think it would likely be called Tadjidi by its own followers (pretty much every Islamic revival calls itself that), Sirozi by academics and neutrals and 'Ilantrabi' by its detractors, the latter trying to emphasize its base origins. TBH I don't know enough about Islamic jurisprudence, do you think it could form a fifth madhab?
So far I'm really curious to see how the Trapezuntines can get out of this hole they've gotten themselves into since David's death. Evangelos is clearly not the leader that will get them out of it (in fact, he seems to be exacerbating the situation), so maybe we'll see someone else restore what was lost. Luckily, their neighbors are either too weak or distracted to capitalize on the collapse of the Trapezuntines, so that's a plus.
As for the issue of republicanism, I don't think the Empire should become a Republic, at least not in the near future. It'd take some serious radical changes and the dismantling of the old order for it to even be possible, and I doubt this will be a popular choice for practically every Roman regardless of their social standing. Constitutional monarchy is possible but abandoning the Emperor seems rather unlikely.