All the pro-Greek camp needed to do was adduce Tzetzes—or would that make it Turkish? 
What the performers do, if I’m hearing it correctly, is extend the (stressed) penult of each line. The klarino sets up the rhythm at the outset. So we get a basically uniform beat throughout the piece, with stress on the even syllables—a rising rhythm, modified at the end to give a falling close.
Swapping out stress for quantity, this corresponds exactly to the iambic tetrameter familiar from Old Comedy.
E.g. Aristoph. Frogs 905-970, Dionysus setting up the great contest between Euripides & Aeschylus:
ἀλλ’ ὡς τάχιστα χρὴ λέγειν· οὕτω δ’ ὅπως ἐρεῖτον,
αστεῖα καὶ μήτ’ εικόνας μήθ’ οἷ’ ὰν άλλος είποι. κτλ.
Empty time is often postulated at the end of each line (hence “catalectic,” “stopping short”), but I wonder whether in fact this modern Greek folk practice, elongating the penultimate syllable and running straight on to the next verse without pause, better reflects the ancient rhythm?
Wouldn’t that be nice?