The city of Smyrna had either a Turkish plurality but Christian (Greek and Armenian) majority (George Horton), or outright Greek majority depending on the source (Henry Morgenthau & Trudy Ring). It was also a cosmopolitan city, with many thousands of Europeans, Americans and Jews, which backs up the numbers which indicate that a Turkish/Muslim plurality does not by itself imply a Turkish/Muslim majority. Outside the city, the Turks were the majority of course.
Nassirisimo, what you have cited is the Ottoman census of 1914, which cannot be accurate as (a) Greeks of the Minor Asia coast were already under persecution by the Ottoman state at the time and (b) it has inaccuracies, for example it underestimates the Greek population of Eastern Thrace by 35,000.
@OP, does the population exchange include Thrace and Constantinople as well? If so, we can assume that the OTL 1.2 million refugees stay in or go (depending on where they were before) to the newly acquired places instead of mainland Greece. Moreover, the 120,000 Greeks of Constantinople will stay where they are, however with a 1919 you don't get to save the victims of the Genocide. So, we're talking about 1.3 million Greeks in Eastern Thrace, Constantinople and Smyrna plus, roughly speaking, and according to the official census since that's what I have available at the moment, 130,000 Armenians and 95,000 Jews. 850,000 Muslims from Eastern Thrace and Smyrna would go to Turkey. Therefore, you're not going to see a depopulated Eastern Thrace or Smyrna, but a problematic demographically Northern Greece and a much smaller Athens, where refugees mostly went to OTL. However, I don't think Constantinople would be included in these arrangements, as its population would have dramatically dropped and an exception would be made so that, for example, a portion of Turks (up to half, I imagine) may remain there.
The problem is, the Smyrna zone was a very bad place for a defending army. Sooner or later, a new war will erupt and it will be impossible to defend all of it. Therefore, either only the city and a small perimeter around it should be given to Greece or it should be made an autonomous city under either Greek or Turkish sovereignty, kinda like Hong Kong.
As for the Church, it will see its influenced increased for a small amount of time, but diminshed long term. The gain of Constantinople will gain many points for the church but eventually, as per OTL, people will become less and less religious and more secularised. There would also be conflicts between the Church of Greece and the Patriarchate on matters of territorial jurisdiction.
As for how to actally get such a scenario, you need not just a Venizelos government, but a different negotiation of the Sevres Treaty. He should not have asked for the zone of Smyrna as I said above, but only the city itself and even that could be done away with. Since there would be concerns concerning the defensibility of the city, probably they can agree to create a demilitarized zone in a perimeter of, eg, 10-15kms, in exchange for a cap in the number number of Greek soldier in the city. With this concession, you can probably get the Allies to agree to different arrangements for Constantinople, provided they get enough assurances concerning demilitarization, free passage of the Dardanelles etc. Militarily, the Greek army stays in the city of Smyrna and defends a small perimeter around it with much fewer forces needed than OTL. In Constantinople, just land 1-2 divisions in the city just in case and patrol the Dardanelles with the Navy and Allied help.