I usually find that the only way I will really get to fight the Timurids or the Mongols is to play as a either..
Russia, Turkey, Byzantium, or Egypt.

I know some players will be France or England and take over the Holy Land, but i like to spread my empire out so its not like i have 2-3 provinces cut off from my mainland.

Crusades are worthwhile to amass a horde that goes forth and sacks towns, like a revenue tactic :)

Very surprised to hear the Timurids got to Frankfurt, but they aren't that big of a threat, just build lots of serpentines or ballista/catapults and get urself enough archers, not too much trouble