Ive also had limited success trying to uncover more data about this topic, there is very little data to operate from so we're reduced to mostly speculation and presumption. I personally tend to regard race in the biological sense as being almost entirely irrelevant in this matter, even today, Anatolia remains a melting pot of different racial and genetic combination, yet by in large, people would identify themselves fiercely as Turkish.
Instead, language and to a lesser degree, religion, are perhaps more useful as an indicator of the kind of demographic changes which the peninsula underwent. In 1071, the year of Manzikert, Anatolia might be seen as an almost exclusively Greek and Armenian speaking region, with a healthy dose of geographically isolated minorities, foreign traders and settled Imperial mercenaries thrown into the mix.
By the time of the Ottoman pre-WW1 censuses, Greeks constitute maybe 15% of the population in areas like Pontus, the Western Coasts and Cilica, half that in Konya and Kappadocia and are almost non-existent elsewhere. Armenians are in a similar boat, concentrated in the eastern half of the peninsula, where they made up 20-35% of the population, whilst being almost non-existent outside that region (the exception being Izmir, on the western coast).
At the end of the Greco-Turkish War in 1922, the two countries agreed to exchange minorities (excluding the region of Thrace in both countries, leaving Greece with a population of 8 million, predominately Greek and Turkey with some 22 million, predominately Turkish. The Armenian population didn't fare so well, being reduced by about 1 million during the Armenian Genocide (insert various interpretations here), bringing a bloody conclusion to the wide-scale presence of Armenians in eastern Anatolia. Interestingly, the Armenian SSR began with a population of a mere 750,000, but was gradually reinvigorated with members of the Armenian diaspora.
That appears to be the extent of our knowledge on Anatolia's demographic history, people were Grecified and Armenianised, then the Turks came and Turkicised and eventually most minority populations were evicted along 1922 boundary's. Sadly, the biggest question, the one the OP posed and one I've wondered myself, is how the process of Turkification proceeded, at what point did the populations go from mostly Greek to mostly Turkish. We've had some insight into the process as elaborated by other posters, sadly the details and hard numbers are beyond us.
