The fact that the Byzantines could no longer rely on the Aegean as a virtual barrier on Turkish expansion into Europe was obviously a big blow for them. With a POD no earlier than 1261, ensure that the Ottoman Empire is never able to expand into Europe.
I'm not just interested in the chances for Byzantine survival (already much in doubt due to the resurgence of Bulgaria and the rise of Venice and Genoa in Greek regions), but also of what other powers might be able to fill the vacuum.
In OTL, an earthquake in 1354 drove most of the Greeks from the Gallipoli area, followed by a quick Ottoman seizure and consolidation of the enclave was what allowed the Ottomans to penetrate into Europe. The Byzantines, had they not been tied up in a civil war, might have been able to crush this settlement. Later attempts at doing so, even with outside help, were unsuccessful. This might be the best point in time.
Or, rather, is it possible that the Ottomans could have lost a later war so badly that they were driven from the continent? Perhaps in the Serbian-Ottoman War of the late 1380s? What about internal problems in Anatolia becoming bad enough that the Ottoman project in Europe gets destroyed in the process? Any thoughts?