I personal don't think the Ottomans the Ottoman is a large problem in fact they may offer the perfect oppotunity for a grand master to make his possessions a secular fief. Maybe with the earlier hit, the Transsylvanian Teutonics could adopt some kind of heresy, maybe a kind of proto-Lutheranism like the Hussite or the Waldensian heresy.
Of course if you want to kill the Ottomans, well it was the westermost Turkish statelet, if the Nicean Empire settle converted Cuman, Slavic and Vlach refugees on the frontier, the Ottomans may fail to set up viable state in the area when the Sultanate of Rum collapse. Especially converted Cuman, if they have kept their traditional methods of warfare, may be a problem for Turkish invaders, while the Vlach lifestyle make them hard to push out of a territories unless you really go after them (like the Teutonics does in TTL). As such I could the Nicean Empire's Anatolian provinces survive for a longer time, in fact they may only collapse when Tamerlane invade Anatolia. This ensure that any Turkish state invading the Balkans may only happen after 1400, which more or less mean that they hit the Teutonic at the same time as the Reformation hit, where the Turks protection could be useful, and they end up a vassal.