I was about to say that even though they called themselves Romans, they spoke Greek and the culture and government had evolved into something Byzantine by that point, and no Emperor would ever consider moving the capital west from Constantinople. But...
"Constantine in reverse" strikes me as plausible in the context of after reconquering the Empire of Justinian and having the Pope under the Emperor's thumb, the schism mended, and possessing resurgent military and economic strength, that an Emperor would contemplate making a bid for complete restoration of Imperial control over the West. At that point locating the capital in Rome would take on great symbolic significance even though it had no economic or strategic advantage.
If I were founding an empire and choosing my own capital, I would pick either Sicily, Venice, or Constantinople. Sicily produces enough grain for a capital city to be self-sufficient, while basing the navy there would ensure that no commander on the frontier could march on the capital. Venice is my favorite location in EU, because you only need to control its one sea-zone to protect the capital, while still having easy land access to the center of Europe -- it can project power better than any other location. Constantinople, while not an island, is well-protected by land and easily resupplied by sea, and at the junction of both land and maritime trade routes.