I think the reference is to the spread of Aramaic under the Neo-Assyrian and Neo-Babylonian empires, which was greatly helped by said empires' deportation strategies. I doubt that such a thing would apply much in an ERE context.What exactly are you talking about? I'm not talking about deportations internal to the Levant, I mean resettlement between Anatolia and the Levant or even with Balkans and Levant.
Anyway, I understand that Syriac was a liturgical language for Melkites too, in parts of the Levant. It is true that Miaphysites and "Nestorians" were deeply at odds, more so than each was with the Orthodox church in many cases, but in the Levant, all three accepted the use of Syriac.
It is plausible to imagine Antioch coming fully into a Greek linguistic sphere, but I still think that Aramaics were entrenchd enough.