Indeed, that's why I think the change should be gradual. Things have been sour for quite some time between the churches, but if the actual Schism is delayed, the continuous losses against the Muslims will ease the Byzantines into accepting the Pope. It will not happen overnight, but as they continue to become more and more reliant on Western military support, there may be a compromise they can accept.The Schism was not really a sudden event but more a recognition of the facts on the ground. Constantinople had never recognized the bishop of Rome as the sole head of the church. It was sort of a "let's agree to disagree" thing for a long time before it finally got to a point where that was no longer possible. You can delay the de jure schism but it de facto is going to be there. It will take a major POD for the Romans to actually pay homage to the pope.