Note a POD: Venizelos has total power in Greece since 1912 (that means that Constantine I is somehow out of the game)!
I'm not saying that is conclusive, but there's a lot of chance that it works.
Balkan wars: Greece gains what she did in OTL, but with smaller casualties (no so many frontal assaults ordered by not-so-good marshal Constantine)
1913-1915: With less political turbulences than OTL (missing Constantine), Greece rebuilds faster after the Balkan wars.
1915-1918: Greece joins Entente in 1915 during the Gallipoli campaign, which now has a good chance to succeed, and if that happens the Greek army is in Constantinople (with the Entente troops) probably in 1916 or early 1917, with Bulgaria possibly neutralised or in Entente's side (as was the actual plot by the Entente and Venizelos).
1918-1919: Greece probably now hasn't the obligation to participate in the Crimean campaign of the Russian Civil War, but holds an operation to bring the Greeks of Ukraine to Greece and newly occupied teritories (including Constantinople).
1919-1921: The Asia Minor Campaign. Either with or without Kemal, the Turks are going to react. The outcome of the Anatolian war isn't sure at all, despite the differences with OTL, but: 1. Greece now does not face the dislike of British, French and Russians, 2. The army officer ranks are undisturbed, 3. Venizelos' diplomatic genius can find a way out even if things go badly.
So I can see either Greece hold Eastern Thrace and Smyrna, or just Eastern Thrace at least, with the Greek population (1.000.000) of Anatolia flowing there and Constantinople, which, of course, with Gallipoli, form the international zone of the Straits.
After all these, I can't see why Greece cannot gain Northern Epirus and Cypruss post WW II...
Nevertheless, I can't see Greece gaining the Straits as direct posession, but a "protection mandate" over the International zone is plausible...