The Byzantines had a mass of political maneuverings, infighting, backstabbing and general fun and games going on. The Imperial Court, the Bureaucracy, the Nobility, the Soldiers, and that's only keeping to what was happening within the Empire. Take in the efforts of the Persians as neighbours... They also had the cold war and on/off border skirmishes and outright short wars over a few centuries.
Something that the Sith Inquisitor should have a good handle on. So therefore, someone with knowledge of how that sort of stuff actually happens.. is more likely to produce an interesting setup then someone who has no clue at all.
Every dark-age/medieval state has struggled with such problems.
I just don't agree that there are any similarities between those and the sith empire.
You can't just say that Byzantine Christianity is the same as Force worship and start copy-pasting.
If you really need inspiration there are plenty of modern autocracies that would make for a far better model.
That's mostly a result of Crusader propaganda and a very long history.
Most western kingdoms couldn't even dream of the sophistication and organization of byzantine state and so they didn't comprehend it fully. If we were to examine 1000 years of history of say France or Britain their history has seen as much civil strife as Byzantium.