There were sizable Greek populations in Anatolia until after World War I, and in 1919 Greece attempted to invade Anatolia and annex most of the coast.

This is a map of the territory the Greeks were hoping to recapture

Therefore, while greeks haven't had political sovereignty for a long time in Anatolia, influential Greeks thought they had a serious shot at getting anatolia back as recently as the early 20th century.

If we can point to a general period in which "turkification" (if it had indeed occured) was set in stone in inner Anatolia so that even if the Byzantine Empire were to retake it from the Turks, it would find that the residents would not speak Greek and practice Orthodox Christianity?

The long process of Turkification really began at the death of Emperor Basil II in 1025. During his reign, a grand bulwark of defenses were set up in Armenia to prevent the majority of the Turks from streaming into the heartlands of the Empire. Basil insisted that these borders be heavily manned, or else the Empire was to fall into ruin. Unfortunately, whether due to "incompetence or sloth", his successors failed to follow through with these wise military plans. Although raids from Arab and Turkish riders had been common in centuries past, these were never able to establish any real permanent settlements in historically Roman Asia Minor, and so, Basil's successors never really thought that they were any serious threat to the stability of the heartland of the Empire.

This all changed with Manzikert. When the Imperial army was destroyed in AD 1071, there was virtually no one left to check the Turkish advance. In just 10 years, the Turks overran Anatolia and occupied Chrysopolis, across from Constantinople. During this time, many of the Byzantine people who resided in these lands were either killed, converted, or fled for their lives. This mass depopulation of Byzantine Anatolians, as well as the Turkish desire to emulate the Byzantines by establishing the aptly-named Sultanate of Rûm and the capital at the old Byzantine city of Iconium, was what allowed them to concentrate their power and supplant historically Byzantine Orthodox populations there.

I would assume that at least in times of Alexios I, most of Anatolia must have been "Greek"- but was it irreversible by the time of Manuel Komnenos??

Upon Alexios' accession in AD 1081, almost all of Anatolia had been overrun by the Turks and was in the process of being transformed. Only a select few coastal cities remained firmly in Byzantine hands. Essentially, at this point, the Empire was confined to its historical "Western" provinces in the Aegean and the Balkans. When the Byzantine-Crusader armies arrive over 15 years later, the process of Turkification was already in full swing.

By the time of Manuel I Komnenos, the Komnenian Emperors had succeeded in exerting military control over most of Anatolia, and it is perhaps possible that Byzantine Greeks began returning to the historically Byzantine cities. However, there would have still been fear of Turkish raids, since not all of Anatolia was firmly under Byzantine control. Much of the center of Asia Minor was still in the hands of the Turks, and they made sure not to allow the Komnenians to easily take their lands back.

Overall, though, I wouldn't say that it was irreversible. The Komnenians, especially John, were able to establish a steady history of military success and recolonization, allowing the Empire to regain lost territories. John's untimely death, however, ensured that this was not fully realized. Manuel, while a great leader, seems to have neglected the diminished threat of the Turks in favor of more grandiose plans, such as retaking Italy and Egypt. While he actually might have succeeded with these plans had things gone slightly differently, in the end, these actions weakened the Empire's position. When Manuel finally turned his eyes to the Turks in the 1160s, it was perhaps too late. The Battle of Myriokephalon in AD 1176 was really the last chance for the Empire to decisively drive the Turks from Asia Minor once and for all, but poor scouting and the Emperor's own hubris ensured that what could have been a certain victory was turned into a demoralizing defeat. Manuel's untimely death shortly thereafter in AD 1180 was the nail in the coffin for a true restoration of the old Byzantine Empire under Basil II.

And also an unrelated question, but how much control did the Byzantine Empire have in the Komnenian era of their "reconquests" in coastal Anatolia, Cilicia, Bulgaria and the Balkans? Were they just nominal suzerainty or was it controlled by Constantinople so that a central governor would be sent to the provinces and actually govern them?

Many of Manuel's holdings were fully integrated into the Empire on an administrative level, but they retained much of their cultural identity, and many of them had been gained through marriage alliances. Unfortunately, the Komnenian system, while effective, required the majesty of a powerful Emperor to function, so, when Manuel died in AD 1180, and without a strong heir (Alexios II was only a child) many of the holdings that he controlled rebelled and formed their own independent entities.

According to Vyronis, The Decline of Medieval Hellenism in Asia Minor, the real turning point was the Battle of Manzikert, 1071. The Byzantines would never really exert control or a dominant cultural influence over most of Anatolia after this point.