The Mongols and the Aztecs have all been crushed very early by the Abbasids. The Byzantine Empire has been expelled from Greece by the a bastard dynasty of the Abbasids (they own everything from Morocco to Punjab, and Greece and Anatolia) and they have Carpathia and a lot of steppes.

Now it's 1420 and I tried to use the converter, but it's broken (because it can't handle the custom titles.). So now there are a catholic Teutonic Kingdom in Estonia-Finland and a Waldensian Teutonic Order in the steppes), so I decided to realise the Iberian kingdoms and Italia. when I outnumbered the catholics, the Teutonic Order became waldensian, but the Teutonic Kingdom remained catholic. The game was a bit boring at this point (just a funny thing: the Teutonic Order managed to create a custom Teutonic Order Kingdom in Estonia. I lost some lands, but I manage to conquer a lot and in 1372 I owned all De jure Hispania, Francia, Germania and Italia. It was Iron man so I didn't took the risk of converting while the Abbasids or the Karlings could erase me.

Once I had a respected and powerful ruler, I became Waldesian (and called my Empire 'the Humble Kingdom of the True Faith'). Recently I made a custom Empire out of Aquitaine, Aragon and Andalusia (beginning as duke of Flanders). I think it's easier to convert to a heresy after you have you're empire than beginning as a heretic count.

Crusader kings 2 cathar