The council of Florence and the subsquesnt turmoil the Empire fell in are not represented at all in this game. In1439 a delegation of Greek (and Isirode of Kiev) theologians, headed by the Emperor himself, went to florence to take part in a debate to accept papal supremacy in exchange for military aid. Now while the whole thing was set up from the beggining to let the Catholics win, Genadios was having none of that and counterargumented most of the time succesfully against the Italians. In any case the union of the churches was decided, with Isidore of Kiev and Gennadios ending up in prison upon their return and the whole delegation beeing booed when Greek commoners saw them sailing back. Now in 1446, IIRC, a Catholic delegation came to Constantinople to discuss the final details, but the Emperor was stalling, afraid of his own people. There were riots on the streets up untill then btw. In the end the Turks conquered the city, released Gennadios from prison, installed him as Patriarch and he repudiated the union that was agreed in Florence.
Now in game terms. The Byzantines should start with a huge dissent malus in their provinces, and should have the option either finalizing the union and getting +50 relations with Catholic rulers(which should allow them to ally neighbors even in very hard) and a -50 malus or whatever with any other Orthodox or repudiate the union, losing the dissent malus but getting a malus in relations with Catholics and a small bonus with Orthodoxs. Now finalizing the union should trigger evens for the other Orthdox countries since it was because of that agreement in Florence that the Bulgarian and Russian churces secedded.
