Hypothetically, if we humor the validity of astronomy software associated with classical precession, which otherwise (conforming to reality) would not produce the horizon relative to the background sky, as displayed...
Subject to the integrity of my memory, Khufu did not hang around for the birth - he did the Freddy Mercury "I want it all... & I want it now!" Consequently the Djedi performed some voodoo with the TwoFish-Channel Sandbank to please his majesty, lord.
Let's tidy this up...
Reviewing the children that are born to Ruddjedet, the papyrus tells us their names
1.)'May you not be powerful in her womb, in this name of yours of Userref!' (Userkaf?)
2.)'May you not kick in her womb, in this name of yours of Sahure!’
3.)'May you not stay dark in her womb, in this name of yours of Keku!' (Neferirkare?)
(The bracketed version if allowing Nederhof the benefit of doubt regarding translation: Userref should be Userkaf and Keku should be Neferirkare).
User is a name for Osiris as established above in the discussion on Reusre. Osiris is also connected to the concept of power and of re-birth.
Keku is the Egyptian god of darkness... According to Budge, “Kekui represents that period of the night which immediately precedes the day”.
Bearing in mind Userkaf, Sahure, Neuserre and Neferirkere were Kings - dump the 5th Dynasty names that you deem irrelevant and make a pick between the 1st & 3rd child fancied to be the elder... then consider:
whatsoever on Earth, by whichever means under the Sun and whenever during his lifetime, can Khufu possibly hope to obtain from 'the eldest'? - whomever you determine such to be...
You mentioned the Duat, Sah... where in heaven's name, is Osiris? - legend tells us the gods are born in the East, at dawn/twilight... Isis, Osiris, Nepthys & Seth are not constellations, they are stars - textual evidence associates Isis with the star Sirius. Osiris morphed as a terrestrial entity, died and resurrected as lord of the nocturnal afterworld - he is not the Sun.
That said, the greater astronomical setting, which you attempt to interpret in context of the overall story-play, is not to be discounted. Concerning the Djedi tale however, my bias (expectedly:-) remains with my own interpretation. [sites.google.com]
ps. I enjoyed the imagery depicting the two crowns in a 'two cobra race' in the link you privided