Of interest is the following:
More precisely, the Western Rite, as approved by the Antiochian Archdiocese is a theologically corrected form of worship used by the Latin Church (Roman) or the Anglican Communion. In some Western Rite congregations, the Liturgy may be a Latin or English form of pre-Vatican-II Roman Catholic worship.
And on another page:
One of the myths presently circulating about the Rite of St. Gregory the Great is that it is "Tridentine"—i.e., it is no older than the Council of Trent [1545-1563]. This criticism is made by those who know nothing about either this Rite or the Council of Trent or the Missal of Pius V . In fact, all that was done at Trent, liturgically speaking, was to standardize the worship of the West. This was done principally in two ways:
First, the Council (together with Pope Pius V) suppressed all Western Rites that did not have a continuous history of at least two hundred years. This effectively eliminated all but the Ambrosian Rite of Milan, the Mozarabic Rite of Toledo, Spain, and the Gregorian Rite of the City of Rome itself, sometimes therefore called the Roman Rite. [* Simple variations within the Roman Rite, such as existed among the Benedictines, Dominicans, etc., were permitted to remain, but have lapsed since the liturgical reforms of the 1960s.] In the 16th century the Gregorian or Roman Rite already had a continuous documented history of more than 1000 years. It therefore became the standard Rite of most of post-Schism Western Christendom. Session XXII [17 Sept. 1562] of the Council issued a series of definitions on the sacrificial doctrine of the Mass, but no change in the actual text of the Rite.
Secondly, the Council of Trent standardized the rubrics of the Gregorian Rite. This meant that when and how the celebrant and other ministers bowed, genuflected, turned to the faithful, etc., was no longer left to the whim or personal style of the individual clergyman. For the sake of propriety, detailed instructions about how to actually celebrate the liturgy were drawn up and imposed upon the whole of the Western Church. Most of these rubrics were not new inventions, however. They were mostly adopted from the customary rubrics of the cathedrals and parish churches of the City of Rome and its surrounding countryside towns and villages. This was logical because Rome was the de jure center of Western Christendom. Thus, by the 16th century even the rubrics already had a long and venerable history and were hardly an innovation of the Counter Reformation.
The Liturgy of St. Peter (commonly known as the Liturgy of St. Gregory), is found, substantially as it has been used in the Latin Church until Vatican II (1969)1, in the Sacramentaries of St. Gregory , Gelasius  and St. Leo . The Roman Liturgy is attributed to St. Peter by ancient liturgical commentators, who founded their opinion chiefly upon a passage in an Epistle of Innocent [fifth century], to Decentius, Bishop of Eugubium. St. Gregory revised the variable parts of the liturgy, the Collects, Epistles, and Gospels; but the only change which he made in the Ordinary was by the addition of a few words which is noticed by the Venerable Bede [Hist. Eccl. Lib.2, c.I.].2Since the time of St. Gregory the Roman Liturgy has been used over a large part of the Western Church, and, until 1969, was practically the only one allowed by Rome.The Western Rite is in a confused state in the Orthodox Church. I've realized, of course, that this is often the preferred way of things in Orthodoxy - clearly defined precepts are only deferred to when absolutely necessary.
My criticism of the so-called Western Rite centers on the unstable historical perspective. As I've noted elsewhere, the liturgical observance seems to be all over the map, involving revised editions of Common Prayer, hypothetical reconstructions of an earlier Roman liturgy, and, finally, if I understand the information cited above and the information provided to me from those involved with the Western Rite, the pre-Vatican II Roman liturgy, either in Latin or the vernacular.
The liturgical climate on the one hand speaks of liturgical plurality. On the other hand, it indicates the delicate state the Western liturgy finds itself in the context of the Orthodox Church.
The Western Rite Vicariate seems to have some members with the appropriate appreciation of the old Roman liturgy. Although, it seems there is not enough historical perspective to reject the instance upon a descending epiclesis.
Dom Denis Chambault provides some guidance and a hopeful point of historical perspective and a path forward. By all accounts, Dom Denis retained the Roman liturgy without modification aside from translating it into French. I welcome correction to the contrary if substantiated.
The instance on Byzantine customs or tradition, or the attempt at "restoring" the Western liturgy based upon vague intimations as opposed to hard evidence robs the Western Rite of any legitimacy.
The way forward to legitimacy is rather plain: use the old Roman books. For the Western Rite to have legitimacy, it must use the historically demonstrable liturgy of the majority of the West.