I wrote a couple of pieces about the intriguing structure of the Roman Canon recently. I have found a dissertation on-line by Matthew Gerlach (now teaching at University of Mary in Ohio) who gives a very thorough, lucid and systematic treatment of the chiastic structure of the anaphora that I found persuasive. He uses the modern form of the Canon as the basis for his study.
He also correlates the theology underlying the Roman Canon with the spiritual exegesis of the Fathers, and the fourfold sense of Scripture (literal, allegorical, tropological and anagogical senses). The claim is that there is a strong parallel and even identity between the patristic understanding of the symbols of Scripture and the symbols of the Eucharistic offering. In addition, spiritual exegesis and the fourfold sense is not an arbitrary reading but is integral to the holy commercium or exchange between Christ and his Body the Church, between its past, its present and its future glory. On reading and re-reading this part of the thesis, I found this extremely stimulating and fruitful and will be returning to it again.
There is also a section about Aquinas's Eucharistic theology which is well worth the read. Acording to Gerlach's perspective, the Aristotelian substance/accidents distinction in Aquinas is utilised because it fits in with his Eucharistic theology of the consecrated gifts being sacramental signs (like the symbols of Christ in Holy Scripture). That is the right way round to read Aquinas; not through the lens of Aristotelian philosophy primarily. The substance/accidents distinction doesn't do justice to Thomas's thought on the importance of the figural significance of the bread and wine, the respect that he gives to the sign qua sign.
It is a while since I have read something that brought things together that I thought I already knew and created a sense of freshness and space for the mind and soul from their synthesis.
A couple of tentative ideas have surfaced as I have been reading about the Roman Canon of late, from various sources including Gerlach's thesis.
Chiasmus is a very good structure for memorisation. If one walks into a room to do something and forgets why one is there, the best way to remember is to try to think of what one was doing just before, and then just before that, i.e. to retrace one's steps in reverse. In memorisation of a text, a series of parallels that pivot on the centre of the text is a very helpful aid. Some people argue that chiasmus is a natural product of an oral tradition: linearity is more of a written textual phenomenon.
Might this be some help to solving the problem of the construction of the Roman Canon? If it was primarily a remembered and orally transmitted prayer initially, with at least some chiastic elements (the verbal and grammatical identity of the memorial of the living and dead in the first and second halves of the anaphora respectively is a case of chiasmus staring us in the face, surely), then might its later and final written form - say, in the fourth century - have been so arranged and augmented to preserve and reinforce its chiastic structure?
Here's a speculation.
Just suppose that there were a series of orally transmitted prayers used in the Eucharistic prayer of the Roman church from the early part of the second century, but not all of them in every celebration. Some of the prayers might therefore overlap and repeat what the others said (like the intial sentences of the Te igitur and the Hanc igitur, or the quasi-epicletic material of the Quam oblationem and the Hanc igitur) because they were once alternative formulations. Some (like the central parts of the anaphora) may have been simply invariable. Suppose the original recited formula was something close to the Alexandrian anaphora, with a rough rule of order in oral recitation, so that the celebrant would have improvised some less central parts of the anaphora from a choice of several traditional prayers that were not identical in wording but carried the same euchological meaning in around the same place in the anaphora. The "through Christ our Lord" at the end of each prayer would therefore have a function partly as a brief break from the effort of recall, to serve as a moment of recollection for the celebrant who would then follow the traditional sequence in his recitation of the next prayer.
Just suppose, when the Roman Canon came to be a written text, that several succeding bishops or their clergy, or just one particular bishop, augmented the natural, oracular chiastic form of the prayer as it already stood - there being some very strongly chiastic elements present already, viz. the central part of the prayer from Qui pridie to the Unde et memores, and the commemoration of the living and dead. Some of the variable prayers of similar euchological function were moved around or altered so that the naturally existing chiasmus of the anaphora would be completed as nearly as possible, without violating the integrity of the oral tradition overly, preserving the variable prayers within the new text.
What one would end up with would be a chiastic structure which had some clearly parallel elements, some not so clearly parallel, and a slightly untidy overlap and anticipation within the latter group (because of prayers with duplicate function having been moved from their original position, or two prayers of the same function being altered slightly so that they could both be included). Which is more or less how the Roman Canon reads.