I would point out that the quote from the 'Catholic Encyclopedia' dates from the early 20th century. The fallacy of 'all serious liturgiologists' is undefendable, and is quite dated: it was a few Roman liturgiologists at a period when the German Rationalists were having a most degrading influence on Catholic thought (see 'Northern Catholics' or 'Modernists'). The Ephesine theory returned with some currency a few decades into the 20th c. as comparison with texts has shown that the early Western rites depend heavily on Near Eastern liturgy. "Ephesine" we only know by the local councils describing its replacement by the Byzantine in Ephesus - in all likelihood it was simply part of what scholars consider the 'Antiochian' family. That the Gallican seems to be a Syriac/Antiochian liturgy in Latin would support the Ephesine theory if Ephesine is simply understood as a local variant of the wider 'Helleno-Syrian' liturgy. (which was claimed by the Church in Britain and Gaul - see 'Cursus Gallorum'.) - Aristibule
This article needs reworking. For example, "Gallican" does indeed refer to the rite of ancient Gaul, although it is also used in a broader sense to non-Roman Western rites. It also repeated the inaccurate description of the restored Gallican rite of the Orthodox Church of France as mostly Byzantine in content.