Use the Kizilimak and Buyuk Menderes rivers as a Byzantine frontier and have them focus more on Europe in the late 14th/15th centuries. Marriages as a means of annexation become a trait of both the Hapsburgs and (insert Greek dynasty of choice). Without a strong polity to unite the region it becomes an area akin to how we see the Balkans in OTL and "Anatolization" takes on the same meaning. Egypt expands northward to Kebir river a few times and even as far north as Adana for about ten years bit are forced back afterwards during the centuries-long Mamaluk-Safavid Wars that only ended when Russia threatened to conquer the entire region. Ironically the internacine warfare leads to early adaptations of gunpowder, the printing press, and interesting innovations like an earlier steam engine (though with limited use due to cost and available materials), public hygeine/germ theory being codified and studied, and wider use of soybeans both as food, feed, and fuel source. With the arrival of British, French, Russian, Italian, and Dutch commercial interests the regions division was likely inevitable despite Byzantine efforts to push east and reunite the great Anatolian plains.