Meaning in Structure: What does a literary device mean?

Matthew claims a 14x3 sructure for his genealogy of Jesus; the final “fourteen” has only thirteen names. What does this mean? I’m not going to spill the beans on what I think Matthew is doing, nor give a thorough review of all the questions involved or possible answered. But I want to use this particular structural question here to point up one huge problem for the scholar, teacher, or preacher in narrative analysis of Scripture: the question of intentionality and meaning in literary design. Just because a chiasm or pattern is present (or appears to be present) does not necessarily mean that the center (or alternatively, the bookends) is stressed….there are at least seven reasons why such patterns might be found, and some of these could easily overlap, of course. These are specific for Matthew’s genealogy, but most apply to other literary structures as well.

(1) Aid for memory
(2) Beauty for the sake of beauty-- if you're going to make a list, why not make it interesting?
(3) Deviation from the theme can highlight an important person, story, or concept. Here I would offer the observations of many that there might be significance in the number 41 (Augustine—40 representing Israel, then Messiah), or that the third shortened “fourteen” represents God’s grace in shortening the time to Messiah. Stendahl of course famously thought that Jesus was 13th and “Christ” 14th. Given the “kingly” emphasis of this lineage, we might also note that there were 41 divinely authorized kings over the tribes in the OT. I don’t know if any of this is correct, but I would be surprised if Matt really had “problems counting.” It’s certainly possible that was the case, but there’s a good bit of strategic work that’s been put into this piece.
(4) Utility—ease of use for those who have to sit through a rather long list.
(5) “Order” for the sake of order—perhaps to reflect “divine order”; this is similar to 2) above. The more orderly or sophisticated the literary work, the higher it would be valued, I reckon. For Matthew of course, the number three, seven, and fourteen seem important for religious reasons; 6x7 could be important, some suggest, as some sort of apocalyptic symbolism, suggesting the advent of the “seventh seven,” the truest or highest stage of Israel, or her telos, in Messiah. Luke's genealogy, by the way, suggests that structuring along the lines of "seven" carried artistic or religious significance.
(6) Intangibles: Maybe Matthew had triplets turning 14? Or fourteen-year-old twins and a thirteen-year-old?
(7) Reader invention: Maybe Matthew had no purpose to speak of?!
(8) As yet unknown: the wild card in every scholarly discussion. A great many texts and ideas from Mt's day are unknown; it's possible we'll never know precisely what he intended.

Anyone have anything to add? Anyone wish to cast a vote on Matt’s purpose here?