I have this pet idea of pulling up stakes and moving the whole Byzantine Empire to Spain; claim island territories and Sicily on the way, demolish and abandon your settlements when the Turks get too close. Once the armada lands in the Iberian Peninsula, blitz the place to make up for lost time and Drang nach Osten through the Catholics until you're in a position to recover the now-restored Eastern settlements you demolished.

(Byzantines) - (Mongols) - (Timurids) = (good times)