Let the Byzentines fight the mongols for a while and then help the Byzentines out. If it's at all possible try to improve relations with the Holy Roman Empire.

Why would he help the byzantines out? They are a major rival in the region. It would benefit him in all kinds of ways if he let them rot. If it's true that the mongol armies are just prespawned hordes then it won't matter if he waits to be in a defensive posture before he fights it.

Once the mongolian threat is no more he can then move to a segmented and weak byzantine empire and take all the orthodox territory for himself!