It's a misunderstanding to think that the Chalcedonian Orthodox Churches in Syria once had a liturgy identical to the non-Chalcedonian Syriacs. For one thing, the liturgy practiced by the latter underwent a huge amount of development after 451-- their prodigious number of anaphorae is the most famous example of this, but their liturgy also contains a great deal of hymnographical development and a substantial amount of Byzantine borrowings as well-- especially the genre of the canon, the Qonune Yawnoye, a great example of Byzantine-Syriac cultural exchange.
On the other hand, the "Byzantine" liturgy, also Antiochene in origin, underwent its own development, as much in the Palestinian monasteries as in Constantinople (and even there, the canon's initial development, by St Romanos, a native of Homs, was certainly influenced by earlier Syriac hymnography). Additionally, while no one has edited or printed any of it, we have pretty much the entire modern Byzantine liturgy, as it existed ca. 1200 available in Syriac in manuscripts. I do hope that eventually the Patriarchate of Antioch will assemble texts from these manuscripts such that the liturgy for St Ephrem's Day can be celebrated occasionally in Syriac, to express the deep cultural roots shared by Chalcedonians and non-Chalcedonians in the Middle East. Some notes I've made about 'Byzantine' liturgy in Syriac, as well as a transcription of the Akathist hymn in Syriac, can be found here: http://araborthodoxy.blogspot.fr/search/label/Syriac