(As regards comments, see the first part of this.)
But ... quam oblationem ... the prayer in which the Church beseeches the Father that her Oblation may be given-the-OK (benedictam) and written-on-the-list (adscriptam) so that, being accepted, it may become the Body and Blood of the Incarnate Word ... is not yet a completed sentence, because it carries on qui pridie quam pateretur ... Thus, the Church goes on to recall, in a subordinated relative clause, the Episode, the Last Supper, on the grounds of which she asks that the consequences of acceptance will indeed be transformation.
Qui is an important word in the Church's life of prayer. A common pattern, which goes back to pre-Christian prayer in the Roman and Greek worlds, is (1) to address a deity, then (2) to recall some attribute or undertaking of that deity, and finally (3) to make the intended request. The logic (going back perhaps to a sense that a deity needs to be convinced or cajoled, even threatened or bribed, or that it will consider itself bound by legal precedent) is that (2) gives the reason why it reasonable to ask for (3) with an expectation of success. Latin has a handy little verb impetrare, which cannot be translated by one single English verb because it means to-ask-and-to-get. Impetratio is at the heart of successful prayer in the ancient world ... I don't think a Roman would waste his time praying if he had no grounds to hope that he was in fact impetrating. So the qui, who, which links up (2) with (3) in effect means something very much like forasmuch as. Almost legally, rather as in the preamble to a British Parliamentary statute*, we tell God why our prayer deserves to be an impetratio. And the qui which links the 'Institution Narrative' to the Prayer for Acceptance which preceded it, has very much this character. So, surely, the logic of this entire passage we have been looking at is: Accept our Offering so that it may become the Lord's Body and Blood forasmuch as the Lord himself guaranteed that Bread and Wine, being thus accepted, would become His Body and Blood.
In our Latin shorthand, we think of this as constituting the Verba Domini as 'consecratory', and this is a very sensible way of thinking and talking (the Church of England adopted the same principle in 1662). It is an extremely ancient view, quite possibly going back to when Christians first started to think logically about such matters. Notoriously, it is given vivid expression in the Byzantine East by S John Chrysostom (c347-407); in Syria, Severus (should I call him Saint?) 'monophysite' Patriarch of Antioch (c465-538), shared it (Dom Gregory Dix was dead chuffed to discover this fact in one of Severus's Letters); and it is found in the Slavic East as late as the first edition of the Orthodox Confession (1638) of Peter Mogila, Metropolitan (should I say Patriarch?) of Kiev (1596-1646).
It is true that 'the Great Church of Constantinople', replying in 1896 to overtures of unity from Leo XIII, alleged that "The One, Holy, Catholic, and Apostolic Church of the Seven Ecumenical Councils used to receive [the teaching that] the precious gifts are hallowed after the Epiclesis of the Holy Spirit by the blessing of the priest", apparently thereby implying that the Church and Rite of Rome did not exist in the centuries between Nicaea I and Nicaea II in 787. But this only proves that we Latins are not the only ones who quite often say and do extremely foolish things. Happily, a few years ago a writer in the theological journal of the Moscow Patriarchate declared himself content with the Roman Canon.
It is a shame that the dominant school among the fashionable intellectuals of the Western Church in the 1960s did not share this contentedness.
*I think the English 'Reformers', with their Tudor legalese, would have used the term 'warrant'.