So, this is my version. I did take the position of the Duat from the other tree, otherwise I came up with everything myself. I'm still working on attributions and stuff, so this is far from complete. I started with Heliopolitan theology and added in both Hermopolitan and Memphite theology. With Hermopolitan theology, Nun (the primordial waters) contains the Ogdoad (eight gods who represent the forces present in Nun), the totality of which is represented by Thoth. These are equivalent to Ain, Ain Soph, and Ain Soph Aur on a standard tree. With Memphite theology, the mound that arises out of Nun, ta-tanen or benben (that second Nun is a mistake, I'll fix that) is associated with Ptah. The rising of the mound takes the place of the contraction or Tzimtzum. On that mound is Atum, who creates Shu and Tefnut, who give birth to Geb and Nut, who give birth to the next four. That's the classic Heliopolitan Ennead. The birth of Horus turns the Ennead into a decad.
The paths between the spheres (I'll use spheres instead of sephiroth) is what's known in kabbalah as the lighting flash. It shows the order of emanation from the first sphere to the last. It's the path of the flow of divine energy. In Egyptian thought, this is Heka or magic (personified as a god). In inscriptions, Heka boasts of existing before all the gods and of having created them. Heka could be seen as the logos, the divine expression by which Atum created and continues to create everything. It is the energy which binds the world together. Shu can also be seen as the logos, and these two are interchangeable. In some pictures, Heka replaces Shu in his typical position of separating Geb and Nut.
Alright, it's late and I'm tired. More later.