More kudos on the explanation and word choices here, jedrious. [initiate golf clap]
What I would suggest, if this is the preferred way to go for a 4E Immortals Handbook system, is that we/you think of the different types of entity as something fundamentally
other than what has gone before. I never conclusively did this myself, until somewhere during the early stages of my 2nd Edition college game I came up with a way to explain how a being could be as far beyond a god as a god is beyond mortals.
To explain, consider that most science fiction describing entities that are godlike (or actual gods) describes them as being somehow "made" of energy the same way we humans are "made" of proteins and other molecules acting out a complex chemical dance. Sentient/sapient machines, based in silicon pathways or other computer hardware rather than biological brains like us, are still fundamentally mortal in most such stories even if they have the capability to think and act thousands of times faster than humans can. They are still limited by the physical laws of matter, and this means that they are not truly godlike even if they are capable of causing events such as the destruction of planets or suns. Beings that are just energy patterns, though, wouldn't have the limitations of matter, and would be capable of feats that can only be described as godlike- hence the reason (I suspect) that most sci-fi that concerns itself with the reality of gods postulates that they are beings of energy. Gods are "beyond" mortals because they're not beings of matter- they're beings of energy.
I began to think of this as a scale. Energy, in a way, is
more fundamental than matter- yes, I'm aware that they're really two sides of the same coin, but bear with me here.

Energy is free of the limitations of matter, though it has its own limitations (for example, the lightspeed limit). To go beyond an energy being to a next step, therefore, the question to answer is- What is "more fundamental" than energy? The answer I eventually came up with is that energy (and matter alike) arises as a result of fluctuations in the "quantum foam" that exists at the lowest substrate of reality as we understand it today. The quantum foam is itself a roiling fluctuation in the patterns of probability that define how matter and energy move and interact within the smallest definable zones of spacetime. Consider, then, what a being that were somehow
made of similar quantum fluctuations would be capable of. It would be able to manifest any sort of matter or energy it wished, at any level it could fit within its own inscrutable limits, and do so on a time scale vastly superior even to that of beings made entirely of energy- because as we know even today, quantum interactions have no speed limit. They occur instantaneously, across literally any distance- the speed of light is not a barrier to them. Does this not sound "beyond" the energy beings that are gods, in much the same way that the gods are "beyond" mortals? A being made of quantum fluctuations is, in many respects, a living law of physics.
Thus, I have long defined the "tiers" of entity with these definitions in my games since that epiphany- and the players in my current games are aware of these definitions (in fact they played a significant part in the recent ascension of a PC). Mortals are defined by being entities whose "souls" are housed in bodies of matter; even if those bodies are technically immortal in the sense of not aging or having a set upper limit on their lifespan, the beings are still mortal because if their bodies are destroyed their minds go with them. Gods are not so limited- they are beings of energy who just form physical bodies because it's a convenient way of interacting with the rest of the universe. The loss of a physical body will annoy a god, but it doesn't really hurt it the way it would a mortal. The physical bodies a god forms for personal interaction are its "avatars-" they are not the god itself, but rather masks it wears to facilitate interaction with mortals.
Overgods- which is to say, Sidereals- are beyond even gods. They are beings formed of fluctuations in quantum probability, inhabitants of the quantum foam at the heart of everything, and they form "avatars" of energy to interact with gods the same way gods form avatars to interact with mortals. The avatars of a Sidereal are, of course, gods themselves, and thus fully capable of forming physical avatars the way any other god can- a Sidereal can thus go around disguised as an "ordinary deity" if it wishes to do so.
For the IH, to be sure, it probably isn't necessary to get this detailed- but I wanted to explain the above to illustrate my point. The system of using "points" beyond the Quintessence that an Immortal uses (which themselves are beyond the Experience that a mortal uses) is easier to explain away if we assume that it really does represent something
different than what has gone before. This makes transcendence to the next stage really mean something beyond just getting more of the same, even if in the game mechanics it all works the same fundamental way.
As a final aside, I have little if any idea how to explain what a being "beyond" the Sidereals would be housed in, though saying (like UK) that it represents a sort of consciousness to the universe itself does dovetail somewhat neatly with my own previous definitions.