C.S. Lewis’ argument does have its place. But it is not the only Christian apologetic available to Christians. I don’t believe he was even trying to use it against the Jewish understanding of Jesus but against secularists who tried to make the claim that Jesus was only a good man.
Exactly right. The best Christian for Christian-Jewish polemics I would say is Michael Brown. I have read most of his stuff too. No matter though, even he fails (IMHO) to make the case because even he can not make a square hole round...and he trys very hard.