Jesus the Levite?

The fascinating idea that Jesus of Nazareth may have been from the house of Levi, as well as the house of David, has been in my thoughts for years. When Jesus asked his disciples who men said he was they came up with four Levitical answers, Jeremiah, Elijah, John the Baptist, or one of the Prophets. Jesus taught people like the Levites were supposed to. He did not rule like his father David. The Dead Sea Covenanters were expecting a Messiah of Aaron. Jesus took over from John the Baptist, a Levite man, proclaiming Repent the Kingdom of God is near. The evidence is clear, his mother must have come from a marriage between the house of David and Levi. This book brings a wealth of evidence to the question. The most striking piece of evidence is that of the Second Century Ephesian Bishop Polycrates (130-196). He claimed, in a debate with the head of the Roman Church, Pope Victor I, that the beloved disciple, John, became a priest in the Temple and wore the petalon. The petalon was a headband that carried the phrase Holiness to Yahuwah on it and was only worn by the High Priest. Was John then a high priest? Was he related to Theophilus for whom Luke-Acts was written?