Okay, I stopped my Bulgaria game (the clash between me and the Ottomans looks scary).
My civilization
I made a decent empire: I had all of Moesia, Wallachia, Thrace, Macedonia, Serbia, Illyria and Greece. I had Thessaloniki and Constantinope (guarded by one Horse Archer on start!). I also had cities in Hungary (Belograd), Moldova (Bholgograd or something), NW of Anatolia (Nicea and the city west of Constantinople). You may say I over extended.
I think there was two keys to my relative stability (only Illyria declared its independance, once): 1) Orthodoxy; the stability bonus was, in the end, invaluable (100 faith); 2) I built Manor Houses, Courthouses and Castles in as many cities as possible. I also didn't change my civics much, only thrice: at start; then to get Religious Law and some other civic; then to get Imperialism (which helped too).
What happened in the world
I was surprised Byzantium didn't crumble after I took Constantinople. I'm not sure it's a bad or a good think historically? They did crumble later on, maybe due to the Seljuks.
The Arabs were leading but collapsed around 1100; my guess is on the crusade. I think the Venetians took Jerusalem; they also paid a heavy price for it since they went civil war! Never saw Venice crumble before.
Hungary eventually crumbled as well, due to Austria I think. The Mongols were coming but they didn't do much to Hungary... Maybe me having Belograd (a core province of them I believe) played with their stability?
Cordoba wasn't collapsed when the Turks spawned and Isabella diverted two crusades on them (Cordoba and Sevilla). Not sure they'll survive the loss of both.
Final thoughts
There seems to be an issue with spread out civs like Venezia and Genoa (which had bad stability too).
One thing I'd ask for though is to not make the mod too historical. I actually liked to see Venezia collapse or to see Cordoba still kickin'. I still dream of a muslim Iberia! Most likely won't happen but it's a nice, alt-historical thought.
I'd also like to have a "+X Faith points" tooltip for religious buildings. Also, Belfry and Reliquary don't seem to give points; I can understand it being for balance but it's not very intuitive. I'd suggest making FP a variable value like in SoI (decreasing slowly). Not sure how that'd turn out though.
I like the new stability model. It's a bit harsh for now. But I like the everpresent need of building stuff in the city if you want to expand.