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I showed earlier that these two men were, in fact the sons of Mary the wife of Cleophas, not Mary the mother of the Lord.

Except that explanation won't fly -- because we're talking about two different Marys (three, counting Magdalene, who is not relevant to the discussion) and two different James (three, counting Bar Zebedee, who is only relevant to the discussion in regard to the record of Clement as detailed below).

As previously anticipated and contraverted in my Post (see the footnoted Link), first-cousin James "the Lesser" (son of Mary of Cleophas) was already numbered by name among the Believers and Followers of Jesus as early as Matthew 10:3, whereas James "the Righteous" (son of Mary of Joseph) was still numbered by name among the Unbelievers and Doubters as late as Matthew 12:46-13:55.

Let me phrase the argument in two parts to make it even more explicit:

Jesus' cousin James "the Lesser", son of Mary of Cleophas, had been a Believer in Jesus and a Disciple with Him on His travels since at least Matthew 10 (and implicitly, before then). By contrast, Jesus' brother James "the Righteous", son of Mary of Joseph, came to him from within Nazareth (and apparently was still a member of the household of Joseph and Mary at this time) with Doubts and Remonstrations.
Thus -- cousin James "the Lesser" (a Believer who had been Following Jesus all over the countryside), and brother James "the Righteous" (a Doubter who had remained in Nazareth all this time) are simply not the same person.
What is more, this is further confirmed by the accusations of the townspeople of Nazareth themselves -- who pointed to Jesus' brother James "the Righteous" as an example of a Doubter and fellow Nazarene local yokel. This accusation would have, of course, been utterly nonsensical as "contrary evidence" against Jesus if they were referring to Jesus' cousin James "the Lesser", who was already a Believer and Follower of Jesus since well before this exchange!!

This is even further buttressed in the Linked Article, in the context of the related citation of John 7 :

3 His brethren therefore said unto him, Depart hence, and go into Judaea, that thy disciples also may behold thy works which thou doest. 4 For no man doeth any thing in secret, and himself seeketh to be known openly. If thou doest these things, manifest thyself to the world. [When we consider how Jesus had withdrawn into the regions of Tyre, Sidon, Decapolis, and Cæsarea Philippi, and with what assiduity he had avoided crowds and concealed miracles, these words become very plain. The twelve had been instructed sufficiently to confess his Messiahship, but thousands of his disciples had not seen a miracle in six months. To his brothers such secrecy seemed foolish on the part of one who was ostensibly seeking to be known. They were not disposed to credit the miracles of Jesus, but insisted that if he could work them he ought to do so openly.] 5 For even his brethren did not believe on him. [This verse explodes the idea that the parties known in the New Testament as our Lord's brothers were the sons of Alphaeus (or Clopas) and cousins to Jesus. The sons of Alphaeus (who were first cousins to Jesus) had long since been numbered among the apostles, while our Lord's brothers were still unbelievers. -- J. W. McGarvey and Philip Y. Pendleton,The Fourfold Gospel, re: John 7: 3 - 5

So, allow me this review of my Arguments:

LINGUISTICALLY, the Greek adelphos is not acceptably translated as "cousin"; the word means "brother" and Old Testament Hebraic concepts do not apply in New Testament Greek. The Greek for "cousin" is anepsios and is used as such in the Greek Scriptures (cf Colossians 4:10). The Holy-Spirit inspired writers of the New Testament had a clear choice between adelphos ("brother") and anepsios ("cousin") and the Holy Spirit chose the word Brother.
LINGUISTICALLY, the Greek prototokon means "First-Born Son" and does not mean "Only-Born Son", which is monogene and which is used quite expressly in John 3:16. The Holy-Spirit inspired writers of the New Testament had a clear choice between prototokon ("First-Born Son") and monogene ("Only-Born Son") and the Holy Spirit chose the word "First-Born Son".
HISTORICALLY, the Exaltation of James the Righteous in the Early Jewish Church makes perfect sense if James the Righteous were the eldest half-brother of Jesus, as the earliest Histories and Church Traditions on the matter (Clement, Hegesippus, Eusebius, Jospehus) roundly declare. In fact, Clement specifically states that it was precisely because James the Righteous was Jesus' blood-brother that the Apostles elected him to the "Episcopal Throne" at Jerusalem and "pre-eminence" over the Apostles -- but Clement's record is, again, nonsensical if James were merely another first-cousin of the Lord, of whom both James and John Bar Zebedee were also first-cousins and who were, with Peter, more especially honored amongst the Apostles than James "the Lesser".
And SCRIPTURALLY, last but not least, we can certainly not take cousin James "the Lesser" (who was a Believer and Follower of Jesus during His earthly ministry, Matthew 10:3) and brother James "the Righteous) who was a Doubter and NOT a Follower of Jesus during His earthly ministry, Matthew 12:46-13:55) and arbitrarily fold them into the same person.

Ergo, to tie it all in with the discussion at hand: good interpretive evidence for something very dramatic happening after Jesus’ crucifixion lies in the very fact that Jesus’ brothers didn't believe who He was (would your brothers?) until the resurrection (which would convince anyone!). Suddenly, the oldest surviving sibling is the head of the Jerusalem Assembly of Jesus Movement Jews. -- Jack Kilmon, History and the New Testament

All of which militates strongly against the dogma of "Perpetual Virginity"; but, what is more, against the Romano-centric and Petrine-successionist view of the Early Church altogether.

best, OP