I have a Crazy Idea. (Haven't tried it yet, but it popped into my head when I got a load of Timurid elephants.)

Rampaging barbarians are not my idea of a good time. That and the porous borders are the only reasons why I don't find the Byzantines ideal for campaign purposes. Let someone else deal with smelly nomads from off the steppe, I want to shoot fish in a barrel!

Supposing you invaded Spain.

Take the whole Byzantine Empire, put it on a tractor-trailer and go island hopping. Sweep up Rhodes, Crete, Corsica, Sardinia and possibly Sicily on the way if you have a strange sense of humor. The Turks, Venetians and Hungarians will probably carve up your old provinces while you're away; wish them well. Your eye is on the prize, and the prize is Grenada.

Think about it this way -- the blokes who are best suited to stop Byzantine horse archers are your neighbors at the start of the game: Russia, Poland, Hungary, Turkey, Egypt. The blokes in Western Europe mostly won't get missile cavalry until the Late period, which means you've got the only horse archers within hundreds of miles. Western armies are terrible at ranged combat. Playing Byzantium in Spain means looking at your neighbors and thinking, "that guy would look great with a piece of wood sticking out of his forehead". The Iberian Peninsula is defended by the Andes, which lets you mop up the Spanish, Portugese and Moors in peace and quiet. Walk your way back East. What're they gonna do, excommunicate you?