As has been noted already, all these options are extremely long shots. I'd call World War I the most realistic, provided that it's an ATL version of the war, with a different outcome surrounding Anatolia. You might then see a scenario where the victorious powers are willing to back an enlarged Greece at the expense of a more harshly punished Turkey.
The more realistic option, however, is an ATL where Catherine the Great gets her wish regarding her Greek Plan a.k.a. "Back to Byzantium".
AFAIK, the
realistic part of that plan was to create a buffer "Dacia" kingdom out of Bessarabia, Moldavia and Wallachhia to serve as a buffer between the 3 empires. The "Greek" part was in a category "wishful thinking" which may happen as a byproduct of an extremely successful war resulting in a complete ejection of Ottoman Empire from Europe.
The obvious POD would be Prince Potemkin (the plan's foremost advocate) not getting distracted with a bungled intervention in Persia. He later admitted that this delayed his anti-Ottoman ambitions, and had been a big mistake. If Potemkin realises this at the time, he'll focus on seeing the Greek Plan carried out.
One of the main obstacles to the plan's implementation (leaving aside trifles like British and French opposition) was not the Persian War because it involved the tiny numbers (successful expedition under
Valerian Zubov involved 13,000 and it happened only in 1796, years after Potemkin's death) or even a lukewarm support of Georgia (even fewer numbers) but a person called Georgy Potemkin.
He was great in making the plans and even implementing some of them (there was a criticism related to the badly chosen site of Kherson, wasteful practices in building up Novorossia, etc. but a lot had been done) but in the military issues he was absolutely pathetic above the level of a subordinated commander.
Worse than that, he was extremely jealous of a competition to his military glory. His main and only qualification as an army commander and then c-in-c during the 2nd Ottoman war was his wish to get the only order which he did not have and could not get any other way, St-George of the 1st Class reserved exclusively for the army commanders for the impressive victories (*). Not only did he pretty much screw up siege of Ochakov making it into a prolonged and extremely costly affair but he handicapped Rumiantsev's successful operations in Moldavia by depriving his army of the resources. When he was finally done with Ochakov (and got his St-George), instead of removing himself from the picture he removed Rumiantsev and the rest of campaign was a series of more or less pointless battles and bloody storming of Ismail, which had nothing to do with the "Greek Project".
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(*) By that time Rumiantsev got it for victory at Lagra/Kagul, Alexey Orlov for Chesma, Dolgorukov for conquest of the Crimea, Panin for capturing Benderi; Potemkin was jealous.
The Austro-Russian talks to plan a joint campaign will occur years earlier, as will the actual campaign. Since the campaign in OTL suffered from randomly terrible luck (disease wiped out substantial parts of the Austrian forces), one can realistically say that the ATL war might well go better for the Austro-Russian alliance. In OTL, Austria was also forced to redirect all its attention away when the French Revolution broke out. In the ATL, the campaign would be just about over when that happens.
Catherine, just as her predecessors, had been suffering from a delusional point of view that Austrians can be an useful ally. Forget about the 7YW (when the Austrians could not even provide an adequate supply for the ally fighting on their behalf), in the campaigns of 1735 - 39 (no French Revolution on a horizon) and 1787 - 92 they proved to be more of a liability than gain (to be fair, under Suvorov's command Prince Coburg performed quite well and should get credit for not making a fuss about him outranking Suvorov). Call it a bad fate or whatever you want.
All of these factors could easily conspire to create a situation where Russia creates a rather large Greek/Neo-Byzantine state, with Grand Duke Konstantin as its first monarch. Thus, you get Russia-backed Mega-Greece, and at a time when the oher powers are all otherwise occupied and can't prevent it. That's easily the most effective (and most-likely-to-succeed) way to get the job done.
Yes. If you are Catherine, don't let Potemkin anywhere close to the army command, pick among the available capable generals even if you (or Potemkin) do not like them personally, arrange for a proper supply of your troops (again, don't let Potemkin anywhere close because he was wasteful and sloppy), do not confuse your strategic and "operational" goals, make a maximum usage of the already built Black Sea fleet (for which a lot of credit goes to Potemkin) putting Ushakov in charge from the very start, somehow persuade the Austrian allies to limit their activities to the Balkans and you have a chance to get to Istanbul before the French and Brits became excessively unhappy (or to wait until the French Revolution starts putting all of them and the Austrians out of your way).