The modifications to the Tridentine Mass and the Book of Common Prayer to make them the DL Liturgies of SS. Gregory and Tikhon are not "byzantine" modifications, they (explicite epiclesis, deletion of references to merits of the saints, etc.) are Orthodox ones.
No, they are Byzantinizations. If the Roman Mass ever had an explicit Epiclesis of the Eastern type, and there is no definitive proof it did, Pope St Gelasius likely removed it. It is known that since Pope St. Gregory the Great the Holy Mass has been celebrated without an explicit Epiclesis, Byzantine or otherwise. St. Nicholas Cabasilas, in the midst of the Hesychast battles, was able to see the venerable Roman Canon as sufficient without one, recognizing the Supplices te rogamus as an implicit Epiclesis; that those invovled with current Western Orthodox liturgics cannot is disturbing
If St. Nicholas saw the Roman canon as sufficient without one, he would have seen the need of recognizing Supplices te rogamus as one (as indeed, it is the remnants of the fuller one), now would he, Deacon?
Your confusion, of course, is coming from the Vatican:
The Catholic Church [i.e. Trent] has decided the question by making us kneel and adore the Holy Eucharist immediately after the words of Institution, and by letting her old Invocation practically disappear.http://www.newadvent.org/cathen/05502a.htm
Nihil Obstat. May 1, 1909. Remy Lafort, Censor. Imprimatur. +John M. Farley, Archbishop of New York
Alas! This is just another example of error and heresy that crept into Rome that transformed it into the ecclesiatical community that left the communion of the One, Holy, Catholic and Apostolic Church as it left the venerable Roman canon
It is certain that all the old liturgies contained such a prayer...Nor is there any doubt that the Western rites at one time contained similar invocations....The Roman Rite too at one time had an Epiklesis after the words of Institution. Pope Gelasius I (492-496) refers to it plainly: "Quomodo ad divini mysterii consecrationem coelestis Spiritus adveniet, si sacerdos...criminosis plenus actionibus reprobetur?" ("Epp. Fragm.", vii, in Thiel, "Epp. Rom. Pont.", I, 486). Watterich (Der Konsekrationsmoment im h. Abendmahl, 1896, pp. 133 sq.) brings other evidences of the old Roman Invocation. he (p. 166) and Drews (Entstehungsgesch. des Kanons, 1902, p. 28) think that several secrets in the Leonine Sacramentary were originally Invocations (see article CANON OF THE MASS). Of the essential clause left out — our prayer: "Supplices te rogamus" (Duchesne, op. cit., 173-5). It seems that an early insistence on the words of Institution as the form of Consecration (see, for instance, Pseudo-Ambrose, "De Mysteriis", IX, 52, and "De Sacramentis", IV, 4, 14-15, 23; St. Augustine, Sermon 227) led in the West to the neglect and mutilation of the Epiklesis.
leaving a deficient canon and an insufficient one were it not for the vestige "Supplices." It was not only the Orthodox in the East who noticed the problem:
in the West too (since the sixteenth century especially), this question aroused some not very important discussion. The Dominican Ambrose Catharinus (sixteenth century) thought that our Consecration takes place at an Epiklesis that precedes the recital of Christ's words. This Epiklesis he thinks to be the prayer "Quam oblationem." A few others (including Renaudot) more or less shared his opinion. Against these Hoppe (op. cit. infra) showed that in any case the Epiklesis always follows the words of Institution and that our "Quam Oblationem" cannot be considered one at all. He and others suggest a mitigated theory, according to which the Invocation (in our case the "Supplice te rogamus") belongs not to the essence of the sacrament, but in some way to its (accidental) integrity. John of Torquemada at the Council of Florence (Hardouin IX, 976), Francisco Suárez (De Sacram., disp. lviii, 3), Bellarmine (De Euch., iv, 14), Lugo (De Euch., disp. xi, 1) explain that the Invocation of the Holy Ghost is made rather that He may sanctify our reception of the Holy Eucharist. This is a theoretical explanation sought out to account for the fact of the Epiklesis, without giving up our insistence on the words of Institution as alone consecrating. Historically and according to the text of the old invocations they must rather be looked upon as dramatically postponed expressions of what happens at one moment.
Most dramatically and to the point, the Scottish church after the reformation saw the deficiency and wrote an explicite epiclesis into their liturgy, and when the newly formed Protestant Episcopal Church of the United States received ordination from Scotland (as the English bishops were prevented by law), Scotland gave it on the condition that PECUSA retain the epiclesis, which later became a source of pride to the delegation to St. Philaret of Moscow. That epiclesis of the rite of St. Tikhon would suffice for the rite of St. Gregory, were it not for the insistence of Ultramontanism that the Vatican's rites are perfect the way she dictates them. The insertion of the epiclesis familiar to most Eastern Orthodox serves a necessary pastoral need, both to legitimize the WRO to any EO who would question it, and to signal to the WRO that they have left the heresy of the West for its venerable Orthodox Tradition. Those who are invovled with current Western Orthodox liturgics know their business, unshaken Orthodox witness:
On the other hand Orthodox theologians all consider the Epiklesis as being at least an essential part of the Consecration. In this question they have two schools. Some, Peter Mogilas, for instance, consider the Epiklesis alone as consecrating (Kimmel, Monumenta fidei eccl. orient., Jena, 1850, I, 180), so that presumably the words of Institution might be left out without affecting the validity of the sacrament. But the greater number, and now apparently all, require the words of Institution too. They must be said, not merely historically, but as the first part of the essential form; they sow as it were the seed that comes forth and is perfected by the Epiklesis. Both elements, then, are essential. This is the theory defended by their theologians at the Council of Florence (1439). A deputation of Latins and Greeks was appointed then to discuss the question. The Greeks maintained that both forms are necessary, that Transubstantiation does not take place till the second one (the Epiklesis) is pronounced, and that the Latin "Supplices te rogamus" is a true Epiklesis having the same effect as theirs. On the other hand the Dominican John of Torquemada defended the Western position that the words of Institution alone and at once consecrate (Hardouin IX, 977 sqq.). The decree of the council eventually defined this "quod illa verba divina Salvatoris omnem virtutem transsubstantiationis habent," ibid.; see also the decree for the Armenians: "forma huius sacramenti sunt verba Salvatoris" in Denzinger, 10th ed., no. 698-old no. 593). Cardinal Bessarion afterwards wrote a book "De Sacramento Eucharistiæ et quibus verbis Christi corpus conficitur, 1462, in P.G., CLXI, 494-525), to whom Marcus Eugenicus of Ephesus answered in a treatise with a long title: "That not only by the sound of the Lord's words are the divine gifts sanctified, but (in addition) by the prayer after these and by the consecration of the priest in the strength of the Holy Ghost."
The official Euchologion of the Orthodox Church has a note after the words of Institution to explain that: "Since the demonstrative pronouns: This is my body, and again: This is my blood, do not refer to the Offerings that are present, but to those which Jesus, taking in His hands and blessing, gave to His Disciples; therefore those words of the Lord are repeated as a narrative [diegematikos], and consequently it is superfluous to show the Offerings (by an elevation) and indeed contrary to the right mind of the Eastern Church of Christ" (ed. Venice, 1898, p. 63). This would seem to imply that Christ's words have no part in the form of the sacrament. On the other hand Dositheus in the Synod of Jerusalem (1672) apparently requires both words of Institution and Epiklesis: "It [the Holy Eucharist] is instituted by the essential word [remati uparktiko, i.e. Christ's word] and sanctified by the invocation of the Holy Ghost" (Conf. Dosithei, in Kimmel, op. cit., I, 451), and this seems to be the common theory among the Orthodox in our time.
Why the modern WRO liturgists, now opertating in full safety, should abandon the position held by the Orthodox bishops being starved into submission at Florence, the Orthodox Met. Mogilas restoring a destroyed Church under the heel of the Polish king acting as the Vatican's agent, etc. i.e. when the Orthodox were being rendered powerless but yet holding tight to the Orthodox position-why the WRO liturgists working in freedom should abandon that position I will leave to you to explain.
I know that doesn't comport with your Byzantinization, but we don't do things the way the Vatican does. That is why we are Orthodox, and it is not, and why the WRO is not "reverse-uniatism" (if there is a more PC term, let me know: I've never heard the accusation of "reverse-eastern ritism" for instance). The Orthodox confess what we believe and believe what we confess: you won't see any WRO parish were someone has gone through all the service books and wrote in "and the Son"