Since the Byzantines already have the cross of St. George, thats effectively incorporated unless you wish to double it. Adding the tetragram would definitely give Byzantine feel, and the meaning: King of Kings Kinging? Kings (the verb doesn't really translate), is pretty good for a united Kingdom. After all the Lancasters are the closest thing to heirs of the Palaiologoi. If there are ever four royal titles, it would gain even more significance.
EDIT: I see c0d5579 has a better translation the Greek is (forgive my transliteration): Vasileos Vasileon Vasilefon Vasilefonton