Maybe Zog feels like he isn't cut out to be king and appoints Mehmed VI King of Albania. Seeing as how the Ottoman Empire was a dynastic rather than National polity it meets the bare minimum requirements. Have the TL proceed as an Albania wank from there to appear less lame.
That's a fun idea.
Maybe we couple that with the Turkish Republic being more successful in its Wars of Independence/Restoration and period immediately afterwards.
-Conquer West Thrace, Kavala, and the Eastern Aegean Islands from Greece
-Conquer Republican Armenia without Soviet help (as for the Armenians, maybe France puts them in Syria?) and back up the Democratic Republic Georgia
-Use the Armenian issue to get the French to help the Mosul question be settled in Turkey's favor
Ultimately this restored Nationalist Turkey decides it wants to influence Albania, so it agrees to restore the Ottomans as the (very very nominal) Sultans of Turkey and the "Ottoman Empire" is a ceremonial entity uniting Turkey and Albania like the British Queen is formally head of the Commonwealth.