In the 600s things still hadn't "hardened", but all the pieces were already in place. Charlemagne's coronation was just the cherry on a cake that had been baking for centuries. Men like Stilicho and Odoacre were those who really laid the foundations. The Goths and Lombards had done more to create the West than the Franks, who came to the table a bit later. The compromise modus operandi between German kings and Roman political structures that gave birth to the West was already a fait accompli in the 700s. You are right to point out that a Roman/Barbarian division was still current, but "civilisation" was far more permeable or woolly round the edges by then. Romanisation had an impact beyond the frontiers, so that most incoming barbarians were already a part of the system they eventually took over. You shouldn't forget that Latin-Greek tensions, or centrifugal forces rather, were already being felt in Diocletian's day, either. To call the Eastern Roman Empire "the West" just seems wrong on so many levels. Constantinople was more concerned with the Caucasus, Asia Minor, the Levant and Egypt than with us out by the Atlantic.