Manetho (Epitome of Physical Doctrines) and Diodorus Siculus (Library of History I xi) tell us that the Egyptian priests learned the myth of Isis and Osiris by careful observation of the Sun and Moon. That the myth refers to the month is also, of course, suggested by Thoth stealing the Moon's light to enable the "birth" of the gods. I had completely ignored that interpretation before, since I wanted to focus on Empedocles, but I thought it might be instructive to spend a little while on it.
We will start by following Manetho and Diodorus by assuming that the Sun is Osiris and the Moon is Isis. Plutarch adds (in his fourth explanation of the myth, Isis and Osiris XLIV) that Set is the eclipse and the fourteen pieces in which Osiris was divided are the fourteen days of the waning Moon. Now, the lunar month is twenty-nine-and-a-half days long, and we know that Egypt rounded it off to a 30-day civil month, and that it began once the Moon was no longer visible to the eye, which occurs approximately a day prior to the astronomical New Moon that we now use. This should give us enough to go on, and I've made a chart of the Moon's phases over the course of the month as an aid to following the touch points between the myth and the month (read it counter-clockwise from the top):
On the first day of the month, the Sun (Osiris) shines but the Moon (Isis) is invisible. If we regard Osiris as the soul and Isis as the body, then this is the golden age, where Osiris reigns in Egypt and the soul is pure and has no need of a body.
On the second day of the month, the astronomical New Moon occurs. It is possible on such days for a solar eclipse to occur, and this would fit the part of the myth where Set kills Osiris and hides him in a box (e.g. the Sun is obscured).
On the third day of the month, the Moon is still not yet visible. This is when Osiris's box floats down the Nile, and when Pan and the Satyrs see it and notify Isis. After this, for the remaining of the first half of the month, the Moon waxes and Isis wanders as a fugitive.
On the sixteenth day of the month, Isis finally recovers Osiris, which represents the Moon going full (which occurs approximately a day before the astronomical Full Moon), which is when the Moon reflects the Sun as perfectly as it is capable of and the full descent of soul into body. During the waxing Moon, the soul takes on various "incomplete" or "lower" forms of bodies, but now it is capable of manifesting itself in matter as perfectly as matter is capable of, in the human body which is capable of rational thought and reflective consciousness.
On the seventeenth day of the month, the astronomical Full Moon occurs. It is possible on such days for a lunar eclipse to occur, and this would fit the second appearance of Set in the myth, out hunting "by the light of the Full Moon" and chopping Osiris into fourteen pieces (the remaining fourteen days of the month, representing the various lives the soul has in a human body). At the same time, Horus (the individual soul) is born: while the soul lived in lower forms, it was as a part of a group soul; now, it is an individual and capable of making its own choices (for better or worse).
As the Moon wanes, the soul grows in power relative to the body (which shines ever less completely). On the twenty-fifth day of the month, the Moon becomes a waning crescent, which indicates that the soul is now more powerful than the body (as the fraction of the Moon which is dark is now greater than the fraction of the Moon which is bright). This is represented in the myth as Horus defeating Set the first time, Isis being beheaded and given a cow's head (with horns, representing the now-crescent Moon).
Eclipses are often portrayed as serpents or dragons; I wonder if Horus's men slaying the serpent, or Apollo slaying the Python, is simply a reiterated reference to the defeat of Set (that is, the resolution of the events which the eclipse originally "brought" into motion).
As the Moon continues to wane, the body loses it's hold over it, and the soul gains pre-eminence. At some point during this part of the cycle, Horus defeats Set for a second time, and the soul lives free of matter.
Finally, when the Moon is no longer visible, the Sun is again alone and the individual has rejoined its Source, Osiris rules in Egypt, and the cycle begins again.
I don't think any of these points change the interpretation of the myth at all, but based on the above, it is certainly reasonable to say the lunar cycle is woven throughout the myth, and may well indeed be its source. Further, it ties the myth to Plutarch's explanation of the Eleusinian Mysteries (On the Man in the Moon XXVII ff.), suggesting Egyptian authority behind Plutarch's secondhand account of the Mysteries (though in that case, Horus would be the Moon, while Isis would be the Earth).
Let's tie this to another myth, that of Europa and Zeus. Without considering the lunar cycle, it didn't quite line up—Isis becomes a cow at the end of the myth, while here, Zeus becomes a bull at the beginning—but, of course, the Moon has a crescent both when it waxes and when it wanes, and so the Europa myth lines up pretty easily.
Europa (εὐρύς-ὤψ "wide-faced," referring to the surface of the Earth) is Isis, Zeus is Osiris, and Minos is Horus. Europa being from Phoenecia but ending up in Crete shows the transmission of the myth. Zeus's transformation into a bull is representative of the waxing crescent Moon as Europa (the body) is snatched away from home (the spiritual world) to Crete (e.g. the material world)—here, there is no Set, no enemy, no sin: the "snatching away" is the normal, intended course of creation. In Crete, Zeus transforms back from a bull (e.g. the Moon is full and no longer crescent), and Europa has a son by him, Minos, who, like Horus, communed with his father from the spiritual world and was so righteous that he was appointed judge over the dead.
But wait, wasn't Minos a jerk who demanded human sacrifice of Athens every nine years? Well, Plutarch (Life of Theseus XVI) implies, and Diodorus Siculus (Library of History IV lx) says explicitly, that there were two Minoses: this myth concerns the first, who was righteous (like Horus); while the myth of Theseus and the Minotaur concerns the second, who was wicked (like Set), and presumably represents a further transmission and development of the myth (e.g. from Crete to Athens).