What would be the effects of Charles being crowned not "Emperor of the Romans" but "Emperor of the Western Romans" or "Emperor of the West" in 800, as an attempt to not alienate the Byzantines?
I dont think it would matter in the end. A slight change in the title really wouldnt help the Byzantine problem, as he is still a barbarian upstart to the East.
Plus the Carolingians biggest problem wasnt the Byzantines, it was really the confusion that came after Louis the Pious' death, and the really unclear confusing will that he left his four sons...