DBAHC: Make The Bishop of Rome A Political Figure

OTL, after the fall of Rome in 476, while the Goths had the northern portion, the Patriarch of Rome quickly contacted the Eastern roman empire and asked for their protection. While they were there they also took southern italy, just in case. However, this ended any ideas that the spiritual leadership was ever comparable to the emperor.

Your goal is to make the Roman church an important political institution distinct from Constantinople and Orthodoxy
well, you can do that by "reducing" the impact of the invasion (maybe another barbarian tribe, weaker than the Goths, invaded Italy and plunder Rome) or the Patriarch of Rome just ran away before the fall of Rome...
So many possibilities.
OOC: sorry for trampling on the OP, but IOTL the Roman Patriarch WAS under the "protection" of Constantinople through half the sixth, all of the seventh, and part of the eighth centuries. They tended to be Greek months and two were deposed by the East Roman Empire. So the POD here just doesn't work.

IC: whichever bishop is regarded as the senior bishop in the West will eventually take on the Papal role, and since Roma was one of the five patriarchs recognized by the early Councils you just have to pry Italy from the grasping hands of Byzantium and Rome takes on the historical role of Arles. Good luck with that.