If in doubt you could always ~ event ##### with the cheats to get some mongols if the games failed to give you any or the ones it gave you were rubbish and got beaten back by the cumans.
Then they would run into the pope.
The pope with unlimited mercenaries, bottomless coffers and unlimited demesne of tens of millions of coins, will turn the tide and conquer all the mongols had.
Next the pope would rid the world of mussulmen. And there would be eternal peace, because the pope attacks no christian and no christian would dare be anything but saintly in all things.