More autocratic than any other nation at the time.
Your second point is a no brainer but doesn't really make my suggestion wrong due to Byzantium's history. Byzantium was about to be conquered by the Ottomans but even so many Italian and Spanish merchants were in their little rump of a empire. The revolts were mostly to take the emperorship not to become their own country by and large. No country has had zero revolts that have had a 1000 years of history or even 100 years of history for that matter.
Constantionple was not just a bunch of ruins due to 'mismanagement and economic problems'. It was that way due to the sacking and conquest of the city by crusaders and the subsequent prolonged looting by the Latin Empire. And you think a Byzantium that is restored would leave their city in rubble?
So you think it's better to rely on what was a nation for ten more years? To ignore history for Byzantium is retarded and equivalent to saying we should change France's ideas because they didn't come up with native trading policies, the philosophies, and liberte, egalitre, fraternite for another 200 hundred or 300 years after 1444. If France's ideas should be based on 200 years in the future Byzantium should have that amount of berth as well.
What would you do for Byzantium's unique government?
Probably not more autocratic than the russian states, for example, imho.
Yes and the sack of Constantinople at the end of the fourth crusade was caused by the dethroned emperor Alexios IV Angelos, who diverted the crusade on Byzantium promising to the crusaders a lot of gold (to use it against the muslims) if they were capable of restore him on the throne against the usurper of Byzantium. But then, after the crusaders put him on the throne, he just realized that the empire was out of money and then he decided to not pay them and to leave them outside of the city, starving. So Constantinople was sacked. And also, the crusaders in that case were mostly italians, and just some years before the emperor Andronikos Komnenos ordered the genocide of all the italians residing in Constantinople (the survivors were selled as slaves to the turks, in the name of multiculturality, I believe), the so called "massacre of the latins", italians who were the major "shareholders" of the empire and the one who dominated the maritime trade and the entire financial sector of Byzantium. Economical domination acquired thanks to continue concessions that every emperor made with this or another italian city state, just to receive from time to time the assistance of this or that other Italian navy, so many concessions to strangle their own trade in a financial suicide.
That's what I call mismanagement.
And Anyway, the fourth crusade happened in 1202, but in the XV century the city was again in ruin, and while they continued to rely on mercenaries, the empire had no money to pay the maintenance of many buildings so many of them collapsed, the population was reduced a lot... When the ottomans conquered the city, they rebuilded it from the scratch not because they want to destroy it but because they tried to save something that was already in pieces.
About the rebellions, with "like in Bulgaria" I was referring to the revolt of bulgarians and romanians against the greeks in the
uprising of Asen and Peter, war of liberation who lead to the resurrection of Bulgaria in the guise of the second bulgarian empire.
Clearly not, I don't think that Constantinople would have been kept in rubble, but a restored Byzantium probably would be an empire of his time, it's not like if the Byzantine empire for a miracle recover itself, it start again rebuilding and making races at the hippodrome, form again the schola palatina, people start to dress like caesars etc... All those things were forgotten. Probably a restored Byzantium would have been very similar to a Christian version of the ottoman empire, with probably more western influence, and in everything, even what we perceive as "ottoman dress" was indeed taken from Byzantium, turbans at the time were pretty common between the byzantines for example, and we know that thanks to the italian painters of the reinassance.
Cyril Mango in his book about the byzantine civilization says that the byzantine people at the time even forgotten who was the builder of things like Hagia Sophia, for example, so trust me, the idea diffused in internet that the Byzantines were the true and conscious heirs of Rome, is false.
But they are still a very interesting nation, and their NI already show perfectly what Byzantium was in that period.
Regarding a unique form of government, I really don't know, in terms of gameplay it was a feudal monarchy, plain and simple.
But I like the proposal to allow them to make royal marriages even outside of their religious group, but that's apply only to byzantine princess and *other-religion* rulers, because a byzantine emperor would never marry a princess of another faith, was a problem even to marry catholic ones, in Byzantium.