Do you want Greece as a vassal? Make them an economic vassal. First try to modernise asap, more modern than the Russians. By the 1880s, if you haven't lost the Balkans yet you can start invest in Greece and lobby for a Pro-Ottoman policy. You would get a situation like Russia and Serbia where Serbia was the most loyal (almost) puppet country in Europe. I can't remember a time where Serbia exists and were against certain Russian policies.
The 1842-1858 and 1880-1900 periods had a Serbian government that was more or less hostile to Russia. The 1880s had a particularly severe case of Russophobia. Oh, and the Kingdom of Yugoslavia's relations with the USSR were pretty awful.
But there's still an useful example there: Russian economic involvement in Serbia was basically nil. Austria's economic involvement with Serbia was very large. And yet, Austria was unable to maintain a puppet, or even friend, in Serbia.
Why? It's complicated, but at the end of the day, Vienna's desires and the Serbs' desires were unrelated at best and totally incompatible at worst. The Ottoman Empire would need to be
much less arrogant and more permissive in its behavior towards Greece than Austria was towards Serbia...and there's no reason to assume that would be the case. So even an economic hegemony over Greece probably wouldn't lead to political puppetization.