There have to be AT LEAST three James's, and I can readily prove it.
Catholics believe there were only TWO James's. James the son of Zebedee, and James the son of Alphaeus. But notice, here in the "Jesus's family verse" from Mat 13:55:
"Is not this the carpenter's son ? Is not His mother called Mary, and His brothers, James and Joses and Simon and Judas ?
Ok, we know the James of Mat 13:55 is not James, the son of Zebedee, because Zebedee's wife is Salome, and his OTHER son is JOHN, who is not mentioned in Jesus's family in Mat 13:55.
We also know the James of Mat 13:55 is NOT the son of Alphaeus, because Alphaeus had ANOTHER son, and his name was LEVI (also called "Matthew") and LEVI does not appear in Jesus's family in Mat 13:55.
Mark:2 14As he walked along, he saw Levi son of Alphaeus sitting at his tax-collection booth. "Come, be my disciple," Jesus said to him. So Levi got up and followed him.
So who is the "James" mentioned in Jesus's family?? There has to be at least THREE James's!
I don't think anybody can "prove" it. I don't spend a lot of time chasing questions like these, since they are not of paramount importance, but from what I've seen, most Scriptural scholars, both Catholic and Protestant, attest to two James. Could there be a third one? I suppose. But with the information available, nobody can definitively prove anything. Your weakness seems to lie here:
We also know the James of Mat 13:55 is NOT the son of Alphaeus, because Alphaeus had ANOTHER son, and his name was LEVI (also called "Matthew")
Question. Why do you think these two Alphaeus' are one and the same? Alphaeus also was a fairly common name. Levi was a tax collector of all things! If Alphaeus who many believe is the same as the one called Clopas was the father of James, then it is unlikely that Alphaeus the father of Levi is the same person. I've just never seen among the many Scriptural scholars I've read, Protestant and Catholic alike, where they assume these two to be one and the same. In any event, either way, whatever. Not the most important issue in the Church. No Scriptural scholar I've read will come out and definitively state the solution to the "James debate", I guess that is what you would call it. Most concentrate on there being two James.