From what I can tell, it boils down to the emperor in Constantinople not liking the fact that the head of the Church was in Rome.
This idea makes for a good dramatic plot, but often we find the opposite to be true, that the emperors were much more willing to be accommodating to Rome than the clergy of the East were. The Roman Pope held an interesting diplomatic position, acting as a figurehead for the people in much of the Italian peninsula, and this provided for an interesting dynamic between the Emperors and the Popes. At times when alternative allies for Rome were few, the Emperors could act in a rather abusive fashion toward the Popes (Justinian, for example, and also the Iconoclast Emperors). But when Rome had strong prospective allies (as was the case with the Franks), the Emperors in the East were happy to fluff up deals with Rome for diplomatic benefits.
This is in fact exactly the case with the buildup to the mutual excommunications of 1054. In the years prior certain Latin controversialists began to spread propaganda within Southern Italy (which observed the Greek rite with leavened bread), decrying the perceived “errors” of the Greek Rite. The situation quickly escalated (with polemicists from both sides claiming the other side’s rite to be invalid) until Michael Cerularius ordered all Latin Rite parishes within Constantinople to be closed. It was the Emperor who was instrumental in trying to calm the situation by inviting the Pope to send representatives to Constantinople, so that the quickly escalating religious tensions could be sorted out. Patriarch Michael was rather reluctant to effect a reconciliation, and Cardinal Humbert in the beginning had such strong support from the emperor that Patriarch Michael’s deposition seemed to be an imminent event. However, Cardinal Humbert out of frustration perhaps, began disseminating polemical attacks against Greek religious customs while in Constantinople. This turned the clergy against him, and it became apparent that Patriarch Michael would not be deposed, leading him to his final act of frustration, laying down a bull of excommunication in the Hagia Sophia during the Sunday Liturgy.
Even before 1054, there was a long history of the emperors trying to get Constantinople to be a Patriarchate increasing honor and prestige
A process which was carried out canonically, the canons being written and approved by the bishops of East on multiple occasions.
despite it not being Apostolic
If I recall, that was not an objection detailed by Pope Leo as a rationale for his rejection of Canon 28 of Chalcedon. His objections were on canonical grounds, that this canon contradicted canon 6 of Nicaea.
like the original three (Rome, Alexandria, and Antioch, in that order).
Actually, the ordering of the see of Rome only appears canonically in the very canons which you claim are invalid. Canon 6 of Nicaea does not make an explicit ordering, and the canons which do give an ordering include Constantinople.
They went so far as to try and declare the bishop of Constantinople “universal bishop,” which St. Gregory the Great fought against.
The title Ecumenical Patriarch does not mean that the Bishop of Constantinople was claiming to be the universal bishop. By this point, the term oikoumene took up imperial connotations, implying only that the Ecumenical Patriarch was the bishop of the Ecumenical City, Constantinople. Pope St. Gregory was mistaken in his understanding of the title, as the Ecumenical Patriarchate keeps this title to this day without any pretensions of being a universal bishop in the sense that Pope St. Gregory understood the term. It is in fact rather strange that people should bring this up as an objection, considering that the title Ecumenical Patriarch is not something which Rome had signaled that it views as being an impediment to union.
Also, it bears pointing out that everytime the two separated sides got together in Council to work out reunion, all disputed issues were found in the Catholic Church’s favor. Unfortunately, these reunions were short lived.
There are only two reunion councils to speak of, and one of them, Second Lyons, only had a small Imperial delegation from Constantinople, and the Emperor had to install a pro-union Patriarch in order to have it enforced as part of imperial religious policy (so much for the claim that the Emperors were the cause of the schism, in this case Emperor Michael VIII was the main driving factor for union, and the union quickly dissolved upon his death). At Florence, only about two dozen Eastern bishops were present, and the council, while approved by a majority of those present, was not received by many of the bishops in the East as legitimate. The representatives of the Catholicos of Georgia, for example, left without ever signing, and the council was never approved by the Georgians. Amongst the Greeks, the bishops outside of the very small territory of the empire mostly resisted the council.