Wasn't there a strong pocket of Nestorian Christianity out that way? Any chance of a Nestorian step empire? Would make for an interesting series of church controversies and might change their focus (IE: they might go through Russia into Persia with the ultimate goal of seizing Baghdad and reuniting with their Nestorian bretherin in Mesopotamia). I'm very intrigued by this possibility but I can't remember how strong Nestorianism was on the step.
Some of the Mongol sub-tribes were Christian, as were many of the wives of the Mongols.
Some of the Il-Khans (Mongol rulers of Persia) were Christians in their youth, but became Buddhists or Muslims as adults. Probably the best chance there.
So bring on the Nestorian steppe empire!
Possible theological controversies:
1. How divided are Jesus's humanity and divinity? Did God the Son die on the Cross? Some Nestorians apparently did not believe God the Son did not die, but only Jesus the man.
2. Universalism--many Nestorian theologians were universalistic (Isaac of Nineveh is the only one I can remember).
3. Nestorian steppe people used koumiss instead of wine for Communion. Bet some people are going to be annoyed.
4. Polygamy-Did any Nestorians practice polygamy? I know they didn't in the early days, but some might have picked it up from Muslims.