Here is your challenge, find a way for the Bishop of Rome to remain a bishop instead of becoming the Pope of Western Christianity leading to no east-west split
I'd say have someone think up the idea of the Councilliary Movement early on. The problem was that after 500, Rome was one of the few real urban centers so you need to make places that can be prestigious enough to have western rivals to Rome. Perhaps Chalemagne can appoint a religious figure for the Carolingian Empire instead of being crowned by the Pope? I think Milan and Ravenna are too close to Rome for it to work for them.I think the real key to keeping the papacy as just another Patriarchate is to have more than one Patriarch in the west. The East/West split is pretty likely to happen unless you seriously alter European history, but keeping the Western church multi-polar would keep the bishop of Rome from asserting his primacy in any major way.