First of all Josephus was a Jew, Israelite, Hebrew, whatever you want to call him, and therefore if he did mention Jesus, as I believe he did, he would not have called him Christ, but Messiah as that is what the Jews were waiting for; and no one said that Josephus actually thought Jesus was the Messiah. Being Jewish, I doubt that he did. He mentioned Jesus as one that was claimed to be the Messiah by Jesus' followers, later called Christians.
All the men you mentioned came after this and being that Josephus was not Christian and only mentioned Jesus, did not write lengthy about Jesus, I doubt there was really any reason for them to have mentioned Josephus and the bit that he had written. Especially, being that has you said he is said to have mentioned James the brother of the one called Messiah.