I feel relatively confident that the God-of-Gods and the Cubit/Zero-God are the same thing. The only reason I think there's the level of confusion here is because the most in-depth description of the God-of-Gods we get is from Koringhus, a Dunyain, who very explicitly isn't thinking about/framing the God-of-Gods the way a human would, but rather from the perspective of a Dunyain. I think trying to divy up all these interpretations (God, God-of-Gods, Zero-God, the Cubit) into distinct entities is actually part of the "lesson" of Koringhus, and also hits thematically, on the entire concept of Mimara being a vessel for the God. Kellhus actually seems like an example of this -- he states to Proyas/Akka (can't remember which) that the GoG is merely the "witless sum", while also claiming to the Mutilated that he is an Inverse Prophet -- bringing word of Man from the Temporal to the Eternal. Yet it is Mimara who is ACTUALLY doing this (and indeed this dovetails with her belief that she actually is what Kellhus claims to be).
This also comes down to how I imagine the Gods/Outside and their utilization of a human vessel in the World. I tend to think that trying to envision the Outside as any kind of "dimension" analogous to something in our world may be a bit "overthinking" it, perhaps. The Outside seems like an amalgamation of a Noosphere and theological ideas of the Pleroma.
Specifically on the Gods and their use of Vessels, this to me seems like RSB's implementation of the ambiguity of the Soul or Consciousness which is prominent throughout the series, but finds itself most apparent when we look at Vessels.
Basically, the "Outside" really is just sort of the "Inside" -- that is, inner space, the Noospheric subjective realm, in contrast to the actual Outer Space (the Void) that is literally outside of Earwa. And so when it comes to Vessels -- Psatma, Cnaiur and Kellhus, Mimara, and in a weird way even Kelmomas -- there is no actual difference between the Soul of a Vessel acting is it would, and the Vessel's "possession" (an imprecise term, according to Oinaral, and I think he's right) by a deity.
In other words, a person doesn't become a Vessel for a God because the God just picked that person. Rather, one becomes a Vessel for a God when the nature of their Soul is in unity with agency from the Outside, including their thoughts and feelings (their Desires, which I suspect is the real spiritual weakness of the Dunyain). All of which, again, are elements of what we could call the Inside, or the Inner Space. So, Kellhus and Cnaiur becomes Vessels for Ajokli because the quality of their Souls coincide with the qualities of Ajokli. Same with Psatma and Yatwer, same with Mimara and the God-of-Gods.
This resolves conundrums like "is Mimara actually granting Absolution, or is the God?" The answer to this (or any other similar scenario -- Kellhus and Cnaiur with Ajokli, for example) is that it's literally both at the same time, because they're actually the same thing.
It also applies even down to the No-God and Kelmomas. The No-God doesn't choose Kelmomas to be its Vessel any more or less than the other Gods "choose" their Vessels. The Gods simply manifest in those Souls which coincide with their own, and vice versa.
Lastly, I think the folks theorizing that Inchoroi Progenitors knew of Damnation/the Outside but simply viewed it in scientific rather than spiritual terms are on the right track. The glossary for TUC supports this pretty well, wherein the Inverse Fire is described as something like a Post-Material Interface Device or something (can't remember the exact wording), but to me -- along with the other stuff people have brought up -- pretty clearly implies that the Inchoroi did not view any of the metaphysical aspects of the Universe in a spiritual manner until they actually got to Earwa, where they directly witnessed the way meaning takes precedence over existence in a more extreme capacity than they previously thought (likely the most immediate indicator being the observation of sorcery as used by the Nonmen).