Genghis Khan as founder/prophet of a major religion

Let's imagine a Muhammad-like Genghis. While remaining in a fully Tengriist environment in general terms, he makes himself the drumbeater of a new religious movement, confusely accepting some tenets from other known faiths/philosophies - revelation, scripture and strict monotheism from Islam, sanctity and martyrdom from (Jacobite/Nestorian) Christianity, unity of the social fabric from Confucianism, etc.
It is likely that his successors will manage to keep the Mongol Empire fully together for longer than OTL, with a religious underpinning. Say, to 1388 (OTL, the razing of Karakorum). Then slowly, the provincial governor will become satraps, and later full sovereigns. Among them, there won't be any converts to other religions, no more than Islam ever had a sultan commit apostasy.
Reasonably, what area could be "Mongol" in religion by now? How far could they go in respect to OTL? Would thing get easier or more difficult for them? And where?
Discuss.
 
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