May I contribute to the conversation with a couple of parameters:
1. Decapitating the Patriarchate (or don't re-establishing it in 1453) and the high-rank orthodox clergy, would contribute eventually to more coversion of Greeks into Islam, but in the same time, it would push the rest of the Greeks to the arms of Catholic Church (probably in the form of Hunite Church) and eventually turn them into a fifth column of a Pope and Castillian crusade. The problem is that this is a situation we cannot say how it would develop.
2. There's trully a very large number of muslim Turks with Greek origins (can't be described as "ethnic Greeks", though), summing up to 20 million or 20% of Turkey's population today (can't remember which, but it's the outcome of a German research in mid' 1990's -IMHO exagerating).
It is thus possible the bulk of them to form a separate state, which is islamic and have some greek elements in order to call it "Greek". IMHO, one good point to create this is the 19th c., by having a different development of Greek nationalism, as follows:
Even thoug the first ideas of the Greek nationalism were absolutely influenced by the western models of nation-building as it was formed during the Enlightenment Era, and all included the creation of a separate Greek state, there were some scholars in the environment of Fanari (the district of the Patriarchate of Constantinople) who claimed that the Greeks, along with the rest of the Christians, could improve their status within the Empire more than by breaking from it. They carried on with this policy until 1923!
After the emerge of the Greek Kingdom, the distance between those two ideologies deepened, even more during the Tanzimat. Their possition, though was worsened because of the schism of the Greek Church, which lessened the power of the Patriarchate, and led to the emerge of the Bulgarian Exarchate, and thus to the "Balkanization" of the Balkans.
If the infiltration of the Greek-state based scholars into the Empire during the Tanzimat period could be limited, I could see a lot of the Greek-origin and speaking muslims of the Empire to gain some concience of differentiation from the muslim Turks of far Anatolia, building up a quite different education system (this was easy until 1923). Again, it is not easy to forthsee the developments, but the possiblility of a Western Turkish state (containing Eastern Macedonia, Thrace, Propontis, Bithynia and Ionia at least) with elements of Greek, or rather more "european" culture is apparent, starting from something equivalent to the New Turks revolution and completed after the inevitable WW I, regardless of the Ottoman stance during it.