I tried a timeline based on this. Venizelos wins the parliamentary battle and Constantine abdicates mid-1915 and Greece joins the war. It is enough to go into southern Albania, help the Serb army and a lot of refugees to retreat (and conveniently establish control over southern Albania). The Greeks get stuck in Trace and Macedonia against the Bulgarians though. The Gallipoli forces are retreated to Thessalonika and add to the Greek war effort.
IOTL, the Entente promised anything off the Ottoman Empire the Greeks wanted. We all know that a mountain of promises become a mole-hill of actual results, but it will probably be better than what the Greeks got OTL since they are fully in the war a lot earlier.
The war against Bulgaria ends 2-3 months earlier, but the Greek army is in much better shape. Not only have they had support from the Serb army and the Entente Salonika forces, but also some Italian troops (that were landed in Albania IOTL).
My idea is that Wrangel's southern Russian white and a lot of Russian refugees end up in Greece (brothers in faith, closer to Russia to go back etc). The Greeks also have very good relations with the Kingdom of Serbs, Croats and Slovenes due to helping the Serb army and refugees (some of which stayed behind) during the war. Entente supplies and extra infrastructure built by them during the war to supply their and the Greek and Serb forces in Greece also means Greece has a better infrastructure and industrial situation. Most of the rich Russian whites end up in Greece and Greek Anatolia instead of Paris, London and Yugoslavia, giving the Greeks some more resources.
The Greeks, with the aid of Wrangel's White Russians and a legion of Serb volunteers and supplied by the Entente go to war with the Turkish Republic. They have better positions from the start and a much larger navy. No monkey-bite either.
The Italians also try to force their part of Turkey, but are defeated and withdraw 1921-1922, which contributes to the fascist takeover. However, the Turks have less men to face the Greeks and White Russians with, and the Greeks win. They take Ionia, from Nicea to Smyrna, the straits and Istanbul as well as Turkish Thrace.
Yes, ethnic cleansing happens. It happened OTL too, called a "population exchange". Atatürk will force Armenians and Pontic Greeks to the Greek part of the country, while the Greeks expel Turks and give the land to Greeks and Russians. It will be much more severe in this timeline, but the grand powers did not give a damn about the same thing when it happened to the Turks and Muslims all over the Balkans after the Balkan Wars, why would they care now?
Greece becomes a junior Entente partner, more or less a client state for British interests in the eastern Med. As a reward, they are given Cyprus (the British had a habit of giving away land they did not really need to loyal small allies, they gave Greece Corfu and the British Ionian islands in 1862), but of course the British maintain a 200-year full basing rights contract, but the Greeks can draft troops and levy taxes from Cyprus.
The British also pilfer away some older ships to the Greeks as the Washington treaty starts. The Greeks are not part of it, but are so much in the Entente/Allied camp that the Brits can count on them in any confrontation in the eastern Med anyway. They probably get HMS Erin and HMS Agincourt and some cruisers. They were supposed to get the Turkish navy in the peace, but Yavuz was sunk by the Turks rather than captured, so they get the ex-Turkish dreadnoughts instead. The Greeks also have the General Alexiev battleship - the white Russians sell or give their ships to the Greeks in exchange for land in Greek Anatolia to establish themselves as rural gentry again.
The total population of Greece in 1925 is something like;
6,5 million Greeks
0,75 million Russians and other whites.
1 million Turks that stayed behind despite ethnic cleansing
0,5 million Armenians
0,1 million Albanians
0,05 million Serbs
This scenario probably means an axis Turkey thirsting for revenge, a hostile Italy and Bulgaria but a very friendly Yugoslavia, Britain and France.
My scenario may very well be ASB, but I think it is the most likely Megali scenario. Post-ww1 is the only time the Ottoman Empire or Turkey was really weak enough for the Greeks to challenge it and get something out of it. At the same time, my scenario makes Greece much stronger and much more supported. It might not be enough anyway, but I think it makes one of the likliest scenarios.