Managed to get going in the end.
So for like 4 generations I had no progress. I had schemes to inherit a couple of counties but those went nowhere. But from the third generation on I had the hellene secret society running, and it got almost 100 members in the end. But with the fifth guy I got stuff running with a bunch of merceneries I was able to declere independence from the duke of Hellas (in 769 Byzantium controls only one county in the duchy of Hellas. The emperor had then essensially no other choice but to grant it to me as a viceroyality, but I lost it when more de jure territory was conquered) (also that's why he got known as "the traitor") and got my wife to be duchess of Achea.
In the end the only part of that that mattered was getting to become a direct vassal of the emperor though (at one point I was the vassal of a duchess that was a vassal to the king of Trebizond, so many steps away from the emperor). When I noticed the emperor had secretly converted to hellenic, I decided to openly adopt the religion. With that I guess I got a lot of popularity, and with only a few bribes I became the leading choice to inherit the empire. I didn't waste time and got the emperor assassinated and inhereted the empire. At the same time, the Abbasids collapsed due to decadense.
I then started to reconquer a lot of land (the previous emperors had even managed to lose Constaninopel) and revoked territories where I could, and placed relatives there to ensure that no matter who got elected it would probably be someone in my dynasty. I got a long way, but in the end there was a massive "overthrow ruler" revolt. I then decided to give in to that, because that just makes me play as my heir.
However then, there was a slowpox epidemic and I didn't get to shut the gates. The prompt said I couldn't do it while doing special activities, which I mean I wasn't doing, but I ended up dying shortly after that. I had managed to get the Traitor to be elected heir, but he suffered the same problems and also died of slowpox soon after (he also ended up getting morbidly obese (in general I've had a lot of fat characters this game, but only like a couple in the zun game)).
Now was the problem: even though a lot of people had converted to hellenic, not everyone had. And this new guy I got was Iconoclastic. I sort of ragequitted then (again not seriously, I had played for several hours and felt like taking a break anyway). I'm conflicted on whether to try and restore a savegame, or kill my wife, get a hellenic one, and use that to convert to hellenism.
Also I've never had the imperial diadem. I've found some guy in the realm has it, related to one of the previous emperors. I've wanted to try and get it, but I've not prioritised it and have focused on warring and installing family members to titles instead.
Also made a stupid custom family seal because I only started with a generic one (unlike for example the zunbils who get a unique one)
however, more important than any of that is that the duke of Abkazia identifies as a horse
(I've gotten about all of Anatolia since this screenshot was taken)