Unless I miss my guess, you are relying on some "traditions" as well: based on his tribe, we know when he served and when he was struck dumb and when John was conceived.
Do we not know that from a "tradition of men", i.e. which tribe was serving when the Temple was destroyed?
John would have been born on Pesach. Most Jews believed that Elijah would come at Pesach to announce the coming of the Messiah
Most Jews believed to me sounds like a tradition of men.
There seem to be other man-made assumptions in your exegesis as well, so I'm a little puzzled by your anti-tradition attitude, especially considering--as any good Jew knows--the oral tradition is not something to be discarded as if it were a meaningless distraction from the Holy Scripture.
Do we not know that from a "tradition of men", i.e. which tribe was serving when the Temple was destroyed?
1 Chronicles 24:7-18