One cannot but be amazed at the stupendous exploits of Graham Phillips. According to his books, he has located one of the tablets of the Ten Commandments (in England), the tomb of the Virgin Mary, the Holy Grail, and other ancient objects. He has also revealed the true identities of William Shakespeare, Robin Hood, and King Arthur. He has solved other various mysteries, including the mysteries of the Ten Plagues in Egypt. Now, he has revealed the true identity of Jesus. And they say that Bible-believing Christians are gullible. To claim such a string of discoveries takes an amazing amount of chutzpah.
As to his proof that Christ is a son of Herod, we are stunned in wonderment. He rests on the claims of scripture that Jesus Christ is the King of the Jews. Pilate's hesitation and his sending him to Herod along with Herod the Great's determination to kill the baby Jesus is supposed to be solid proof of this relationship (after what you call "a close reading of the Gospels").
But the Herodian family was not even of Jewish stock. They were Edomites, the ancient enemies of the Jews. And, though they were nominally Jewish in practice, they would be the last people to be accepted as proper kings by the Jews. They certainly were not of the line of David. Herod the Great was called the "king of Judaea" (Luke 1:5), but he was not the king of the Jews.
This "close reading of the Gospels" also rejects the absolutely clear statements and descriptions of the birth and paternity of Jesus. That is, while making gargantuan leaps in logic to prove the ridiculous, Phillips totally ignores the exact statements of Matthew 1:16-25 and Luke 1:30-35. I accept the right of you or Phillips to reject the miracle of the virgin birth. However, to claim scriptural authority for doing so destroys all concepts of basic reason. I accept a miracle as true that is clearly taught in the scriptures. Phillips is making up a miracle of his own based on castle-in-the-air assumptions while ignoring the Bible's direct statements.