Since you seem to enjoy the Byzantine area, I will recommend the following two starts. Both of these involve well-developed heresies with unique mechanics, and to boot you will even be able to create a new, much more centralized Byzantine empire. If you do it right, you should find it much easier to control and organize your vassals to your pleasing.
I am sure you already know about the Paulician start in 867, but I will mention it anyways because it is a blast. Just to the East of the Byzantine Empire is the one province Paulician Patriarchate. You will be locked into a seemingly impossible war with the Byzantines from the start, but if you act fast you can win it, as the Byzantines will be pre-occupied with another war involving the Muslims in Sicily. Raid all the things, raise all the zealots, gobble up the petty kingdoms in the Caucuses, and strike the Byzantines or Abbasids when they are weak and/or involved in other wars. Form a new Byzantine Empire that loves to raid and spread the one true faith. This start, while seemingly difficult due to only having one province is actually very forgiving.
Now, for something a bit less known from 1 Jan 1232 - 31 Aug 1239 the Bosnian Vassal of the Magyars is a Bogomilist, and all of his Duchy follows the heretical faith too! This start can be a little more difficult than the Paulician one, but certainly not impossible if you play your cards right. Bogomilism is interesting because it actually has a gradual reformation mechanic that offers all kinds of boons, and there is a ton of flavor that comes with reforming the faith, even building your own Hagia Sophia. Once you manage to break free of the Magyars the Balkans should be in a prime position to be swallowed up. Before you throw off the shackles of vassalage, it might be wise to attack the other Magyar vassal to your West, as I think they control a Bogomil holy site. Once free, Serbia is a good route for expansion, and from here you can very well steam-roll your way into making an anti-feudal (try wrapping your head around that!) Bogomilist Byzantine Empire. There is no sprawling Byzantine Empire in this date, so you can absorb the various successor states and take the crown yourself.
