One of the things that was mentioned on the last Lumen Orientale Conference was this installation of Latin bishops into the East. The retort was the East did the very same thing in the West, and therefore, should be one of those things dropped.
Do you have examples? I mean, in southern Italy which had the largest Byzantine presence, I haven't read so much about replacements of already entrenched Latin bishops with Greek ones. Before the Byzantines came in during the time of St. Justinian, it had only been a few centuries after the end of persecutions and these years also saw barbarian incursions and Arian upheavals. I'm not sure if bishops there in the time of Justinian were replaced Latin for Greek (after all, at that time there were just Romans all), or if over time as customs changed, the bishops in Byzantine territory, formerly on Roman canonical territory were switched to Constantinopolitan authority. That's quite different from what the Crusaders did at Antioch and in the Holy Land.
Unfortunately, I'm not very familiar with this beyond what I gave. I wish I had more information, as well. I can however find the recording and post it with a timestamp for reference.
Father Taft addressed this issue some, but I'll add a bit more based on what I recall from various (secondary sources) on Southern Italian history. Unfortunately, I can't make precise citations right now (search for histories of medieval Southern Italy on Amazon and you'll find the books I read). More importantly, there's a whole trove of information in Italian, which I doubt will ever be translated.
During Justinian's conquest of Italy (where, IIRC, he was technically still recognized as rightful emperor by the Ostrogoths, who were theoretically reigning in his name), the Empire may very well have appointed bishops from Constantinople to sees that fell under their military jurisdiction, but I am not aware of any specific cases and so I can't compare them to the ouster of the "Greek" Patriarch of Antioch by the Crusaders and his replacement with a Latin Churchman.
The big complaint against the Empire is that it took all the Italian sees under its political power and removed them from Old Rome's jurisdiction to Constantinople as a move against Old Rome's anti-iconoclasm. This was not only reversed by the Norman Conquest in the 1050s. AFAIC, this is essentially equivalent to what the crusaders did in Antioch.
Later, in approximately the 800-900s, Greek vs. Latin rite conflict were a major factor of Southern Italian politics, as one proxy for Imperial vs. Lombard/German political conflict. Sees and the rites used in the see would switch based on which faction was in charge at the time. I am also told that Old Rome and most other major Italian cities (e.g. Venice) factionalized on similar lines, though Imperial troops never made it that far north and so the pro-Empire party never had that to back them up. This conflict essentially ended with the Norman conquest of Southern Italy and their subsequent invasion of Greece, making the Empire politically powerless in Italy. (this took place at about the same time as Manzikert - in fact, the Norman threat was arguably more serious)
Finally, as far as 1054 goes, Aristeides Papadakis' book The Christian East and the Rise of the Papacy essentially argues that main factor in the schism is the "Gregorian Reform movement" - in many ways a movement to impose Northern European ecclesiastical norms developed in the 11th century - combined with the movement's actualization in the Pope's belief he that he could dictate who should sit on eastern Patriarchal sees once he had the power to do so through the crusaders, and later in the crusades to shore up the Latin Empire in Constantinople.
To my mind, even though there are no longer crusaders and no one would seriously think today of ousting bishops from their sees and replacing them with those of the invading culture, the underlying point is still a legitimate question. Is the bishop organic to his see, and can Rome unilaterally appoint/depose him - even if it's another patriarch, and even if the bishop is outside Rome's "canonical territory" (assuming there is even a limit for such a thing)?