I'm still confused here. Why do you say that Meletius was not in communion with Rome? I have found no where showing that Meletius was excommunicated by the Pope or that Meletius was formally declared a heretic by the Pope.
Kelly says he was not in communion - you may have missed that explicitly saying so.
Meletius was not the Pope's candidate for the See.
Besides being in communion with the Catholic church just requires you to be Catholic and as far as I can tell Meletius was never not Catholic. The problem in Antioch was due to a schism caused by the Emperor Constans after he banished Meletius and appointed Paulinus, and was made much worse due to the Arians and other political factors.
Not quite. The 'schism' was one of the Pope and the Pope in Alexandria supporting Paulinus. Not Meletius.
If you want to suggest that Catholicism accepts bishops not supported by the Pope, that's fine
For people interested, here's a more extensive quote from Davis (highlighting added by me)
"The work of the Council of Constantinople was completed. Theologically, it had carried the logic of the Council of Nicea and cautiously applied that Council's reasoning about the Son's relation to the Father to the Holy Spirit, though confining its statement to biblical terminology. Administratively, the Council continued the eastern practice of accommodating the ecclesiastical organization to the civil organisation of the Empire, sowing the seeds for discord among the four great sees of East and West by raising the ecclesiastical status of Constantinople to correspond to its civil position as New Rome. All in all, it proved to be a remarkable Council. It was never intended to be an ecumenical council: the Bishop of Rome was not invited: only 150 Eastern bishops were present; only one by accident from the West. Only at the Council of Chalcedon of 451 did it begin to rank in the East with the Council of Nicea as more than a local council. Because of the schism at Antioch its first president,
Meletius, was not in communion with Rome and Alexandria. Its second president, Gregory of Nazianzus, was not in western eyes the legitimate bishop of Constantinople. Strong doubts were later expressed about the authenticity of its creed. Its canons were rejected in the west for nine hundred years.
Davis L. D., (1990), "The First Seven Ecumenical Councils (325-787) Their History and Theology", (Liturgical Press, Minnesota), pp128-129
The pope's rep, the oddly named Lucifer went to Antioch
"Lucifer goes to Antioch and consecrates Paulinus.
It was decided therefore that Lucifer should go to Antioch in Syria, and Eusebius to Alexandria, that by assembling a Synod in conjunction with Athanasius, they might confirm the doctrines of the church. Lucifer sent a deacon as his representative, by whom he pledged himself to assent to whatever the Synod might decree; but he himself went to Antioch, where he found the church in great disorder, the people not being agreed among themselves. For not only did the Arian heresy, which had been introduced by Euzoius, divide the church, but, as we before said, the followers of Meletius also, from attachment to their teacher, separated themselves from those with whom they agreed in sentiment. When therefore Lucifer had constituted Paulinus their bishop, he again departed."
Socrates Scholasticus
"The Ecclesiastical History" Book III.6
Thus the Papal person proclaimed Paulinus bishop in direct opposition to Meletius. Meletius continued with his own support in direct opposition to the decision of the Pope's man.
"Now recall that Paulinus is the Pope's man. Meletius continued to hold church services (outside the city walls) during this time. And the two continued in 'office'. One not being the Pope's choice. An arrangement was made that when one died, the other would succeed."
Socrates Scholasticus
"The Ecclesiastical History" Book V.5
Paulinus actually argued from canon law that there should not be a co-bishop!
And of John Chrysostom; continually consecrated by Meletius, he later separated from him WITHOUT joining in communion with the Pope's man, Paulinus.
see Socrates Scholasticus
"The Ecclesiastical History"Book VI.3
"About this period Meletius, bishop of Antioch, fell sick and died: in whose praise Gregory, the brother of Basil, pronounced a funeral oration. The body of the deceased bishop was by his friends conveyed to Antioch; where those who had identified themselves with his interests again refused subjection to Paulinus, but caused Flavian to be substituted in the place of Meletius, and the people began to quarrel anew. Thus again the Antiochian church was divided into rival factions, not grounded on any difference of faith, but simply on a preference of bishops.
Socrates Scholasticus
"The Ecclesiastical History" Book V.9
And as noted John Chrysostom took orders from Flavian (after Meletius' death). Flavian was not in favour with Alexandria nor Rome. Flavian then sent messengers to Alexandria AND Rome to work out peace.
see Socrates Scholasticus
"The Ecclesiastical History" Book V.15
At that time there were several and rival claimants to be the proper patriarch in Antioch. Paulinus was the man favoured by Rome and Alexandria. Meletius was favoured by others. Jerome accompanied Paulinus back to Rome in order to get more support for him.
He was corrected -- in gentleness, but corrected nonetheless.