That's a heck of a good start!
I am pretty sure that the Pope still uses the 'Patriarch of the West' title. As I am sure you know, the office has accumulated titles for 2000 years. As in the title 'Pontiff' which was originally the Roman pagan title 'Pontifex Maximus', an office held by both Julius Caesar and Cicero (maybe even Sulla, don't know about that). The Vatican bureaucracy is called the 'Curia' which is one of the names for the Ancient Roman Senate. Roman Catholic Canon Law is naturally based on Roman Law, most likely Justinian's codification. Rome does not throw out anything useful, a lot like me.
A little hard work by theologians in both churches, a withdrawal of mutual anathemas, a pledge to remember why Byzantium and Rome originally gave their mutual support to the Crusades, forgetting about that little unpleasantness with the Fourth Crusade, and we can work together more smoothly. I know that a little work will need to be done on the issue of Papal Infallibility, but where there is a will, there is a way (just don't ask me how!)