And All The Nations Shall Gather To It has as its very POD that Alexios is not advised to abandon the Crusaders in 1098, and that he aids them in the siege of Antioch. From this, it then transpires that Antioch remains in Byzantine hands, with general Tatikios ruling over Syria as Doux of Antioch. The Byzantine-Crusader alliance holds, the Crusaders march on towards Jerusalem (and indeed set up their own fiefs), but Antioch remains Byzantine and outside the Latin sphere.
This is pretty much the most solid POD I could imagine for a Greek Antioch, short of something that prevents the Islamic conquest of Syria in the first place.