So, your challenge, should you wish to accept it, it this:
Make sure a Nordic dynasty controls the Byzantine Empire for at least three generations. How you choose to go about this challenge if up to you. Is that any chance of a trusted member of the Vangarian guard assuming the position of Emperor after converting to Orthodoxy? Does a Nordic Armada sack the Queen of Cities and install its own Emperor? That's up to you. Go! The only prerequisite is the Emperor is of Nordic culture and the dynasty lasts for at least thee generations (so, no, one-time Emperor takes control and is quickly overthrown by the Greeks after just a few years)