The latest possible POD would have to be a Nicaean state that becomes more Turkified. A state that is able to do for Orthodoxy what the house of Osman did for Islam.
Perhaps a half Turkish, half Anatolian Greek general that understands both sides is able to (with quite a bit of luck) bring both sides together as the Ottomans were able to. A later reconquest of Constantinople seems smart, as well as a greater emphasis on absorbing and co-opting the Turks (or Turkified Byzantines, depending on your viewpoint) into the empire.
Perhaps a half Turkish, half Anatolian Greek general that understands both sides is able to (with quite a bit of luck) bring both sides together as the Ottomans were able to. A later reconquest of Constantinople seems smart, as well as a greater emphasis on absorbing and co-opting the Turks (or Turkified Byzantines, depending on your viewpoint) into the empire.