I'll give that one a go. (There is a lot of Handwavium involved here, forgive me)
1453 ends with an Ottoman near-defeat, that erupts into political chaos - during which the Byzantines manage to take control of the Bosporus and Dardanelles. Hungary, and other Christian nations provide some backing, and some invade Ottoman Europe, forcing some sort of peace that leaves the Byzantines in charge of the straits, and able to pay for some semblance of a standing army that brings the Morea in line properly - furthering the Byzantine Renaissance in the Morea, and allowing Constantinople to become of the the hearts of the Renaissance proper (their Meiji).
With their old knowledge, and an economy on the up, the New Byzantines, with some European backers, retake Greek Europe, with Genoa and Venice getting Anatolian territories.
With Anatolia... pacified, they focus on expanding in Europe, Albania, Serbia, etc - adopting a heavy siege component and gunpowder infantry after seeing the formers success in demolishing the Theodosian walls. This ratcheted up military doctrine helps them reconquer previous territories until they are, alongside Hungary, the defacto rulers of the Balkans. Throw in a marriage that leads to an opportune union of the Byzantines and you have a Balkan Meiji. (And one that might even have cannon-fired napalm to boot if you want to have nightmares).
EDIT : I'll hasten to add that if you want the Balkans, ANY Balkans power to pull a Meiji, it needs to be big on immigration, just to boost tax revenue and manpower. Plus, having a large number of Jews at this point could pay dividends in terms of enabling lending, however unintentional.