St. Augustine doesn't rule out angels that could assume a partially corporeal nature, but his issues with it are how these angels could fall. Now, even if they could somehow assume a corporeal aspect, in order for any kind of lust to be in play, that would assume that these angels did have a sensible part of their being that could directly interact with this assumed body.
I think that the inclination today to reject the notion that these were angels comes from our definition of angels as being pure spirit (without even a sensible part of their being). But I don't know that we can preclude God's having created a type of angel that is in between the purely spiritual world and the material. We see that in one of the Church Fathers who wrote about this that this was the lowest tier of angel charged with interacting with the material world ("to govern matter in all its forms") and stationed at the "first firmament", namely, at the physical boundary of our world. So the Patristic quotes cited by Pax in the OP seem to indicate these Fathers before St. Augustine clearly believing that these were angels.
If you think about the etymology of "angel," it means a messenger. I look at that as meaning that they transition in hierarchical fashion down from God, to higher angels (who are the most like God), to lower choirs of angels, and ultimately to man and the physical world. So they're transitional between God and the material world. From what we know, Cherubim and Seraphim (the highest choirs) do not actually serve as "messengers" because they're constantly in the presence of God. So to call them angels I think simply means that they're lower than God, but then at the top of a hierarchical ladder that extends ultimately to the material creation.
So does it make sense for there to be one more step in the hierarchy? I think it does. It's typically been understood that man is the ultimate bridge between the purely spiritual (the invisible) to the purely material (the visible). But that does seem to me to leave a bit of a gap that could be filled by these hypothetical angelic beings.
So my hypothesis is that these beings were angels in the sense that they were transitional between God and ultimately man and then material creation, that they had a purely spiritual aspect, but also a sensible aspect, and that these were essential to the definition of their nature. Yet, unlike it is for man, it was not of their essence to have this sensible aspect joined to a body, but they COULD assume bodies, of a more ethereal nature, not made from the clay of the earth, but from a more rarefied material (such as which St. Augustine describes), and that these rarefied bodies (optional for them, unlike for man) could then interact with this sensible aspect of their nature, and so they could, for instance experience sensations such as attraction for women and then, after their fall, lust.
And this also would explain how they could fall in "time" as opposed to the angels who, being PURE spirit, had to decide to be either for or against God at the first instant of their creation. Time and movement through space are related to matter, and so is the capacity to "change", so this material aspect of their nature could explain how they could change over time and thus fall at some point later, rather than at the instant they were created.
These types of creatures would also explain all the ancient legends about these "gods" that came from the sky or lived in the sky (up in Olympus). Those "Ancient Aliens" people point out that nearly every ancient culture had stories of these "gods" that came from the sky. Of course, they misinterpret them as having come from other planets, but perhaps, as the one Church Father described it, they came from the lowest heaven (understood as the sky beneath the firmament by the Fathers), i.e. "the first firmament". It would be interesting to re-examine the very interesting findings made by the Ancient Aliens crowd under the supposition that they refer to these types of beings. Many of these stories speak of these gods mating with women, and that the result of this mating were the "heroes", such as Hercules, etc. were the result. And Genesis mentions that in fact the offspring of these "sons of God" mating with "daughters of men" was in fact the "great men of renown" and "giants". Every culture has these stories and legends. So it all starts to make sense. I've long been of the opinion that when cultures had stories like these, it wasn't because they were stupid, such as, "oh, look, lightning ... since I don't have a scientific explanation, it must be some god hurling it down from above" and that there's always something REAL to all these stories. Sumerians have the Gilgamesh epic which is nearly identical to Sacred Scripture's account of the Great Flood, and they had this "god" named Enki (could that be Enoch?) who would go back and forth between the gods and them (precisely as the Book of Enoch describes Enoch ... and of course the name is similar).
This is my current working hypothesis.