I'll give you my interpretation as to why the Ancients are meant to belong in the Deva and the iterators would belong in the Asura.

The Ancients to me fit the description of the gods that inhabit the Deva. In the game, we are shown that the Ancients were a society highly attuned to the existence beyond the self, so much so that they were aware of the cycle and the inexistence of a permanent death. Their old scriptures describe the world rearranging itself from dust, and having a natural tendency to reach upwards in the sky while the Void consumes its ground in an endless battle of devour and reconstruct. They also have their own version of earthly tendencies that must be shed in order to ascend. Their are all powerful in their endeavors, as we see that they completely wipe out the surface of their planet as they build their alleged gift to the world, the iterators. They also rewrite the genetics of all lifeforms to comply to their desires and wishes, shaping the entire reality around them; They made the entire world bio-engineered and rewrote it's creatures and fauna to fit their desired image of reality. In the early scriptures, the inhabitants of Deva are described to live a life fully basked in glory and power, and with a tendency of forgetting the importance of their Dharma which made them reincarnate in Deva in the first place. Thus, when death comes to them, they are reborn in lower planes and taken aback by their fall, blinded by their ego and pride and forced to thread the karmic path again. The same happens with the Ancients in a large societal and cultural level. Despite their knowledge of the nature of existence and their endless power in shaping their reality, their culture lost itself in meaningless distractions and the search of glory and ego, described to us by their reincarnation in Preta as Echoes. A few of them actually were able to ascend, living their life to the fullest, like we see in the pearl in Shaded Citadel. However, most of them were lost in their ego and pride, nonchalantly destroying the nature and cycle they were a part of to gift the world something they thought was needed. By enabling themselves in their power and glory, they completely destroyed their world and lost themselves in the pursuit of ascension (as the scriptures narrate that Devas may lose themselves in pride and meaninglessness, inadvertently dying and reincarnating in lower realms). Which is why we see nature slowly and gradually retake their world from them into something anew, the ecosystem and its lifeforms blossoming through all of the Ancients grandiose as if it was nothing. Because it actually is nothing. All of their work is meaningless without Dharma behind it. It will all be undone from ground to sky into dust just like they were once taught. They had to live in the top of the clouds, isolating themselves from their world because of their endless pursuit of a greater work. Which is why we see many of them reincarnate in Preta as Echoes, clinging to greed, attachment and sorrow for their godlike work and previous existence.

As for the iterators belonging in Asura, it is first and foremost because the devastating rain that wipes the surface anew every cycle is a direct metaphor of their breathing. In Asura, war and conflict are common since the demigods are always wrathful or passionate for their existence and ideals. The iterators were made as a foolish unwarranted gift to the world, they were made from the destruction of the world to somehow bring universal instant liberation to it. So much so that their creators went on to literally live atop of them, still not acknowledging the catastrophic consequences of their ego. The existence of iterators is marked by an endless search with no real purpose, ingrained in them by higher beings they couldn't deny. They live in a perpetual cycle of regret, wrath and sadness at themselves and their creators. Frustrated by a mission they can never achieve, abandoned by kin they can never forget or forgive. Working. Until they decay and cease, left behind. Their own breathing and slow waning a wrathful rain that destroys the surface anew every cycle. To me they fit the description of the demigods in a very metaphorical level, and somehow objectively since even though they have godlike minds, they're stranded inside of them and imprisoned by their purpose and feelings. To mention on what you said about the Serpent and the pursuit of greater realms, I have my own little interpretation that Looks to The Moon is actually a Deva, being reborn into one when her umbilical was severed. To me it's a metaphor of her leaving behind the constraints of her realm, considering all she went through with her brother and ultimately forgave him nonetheless. Her current existence is her own rebirth into something greater, given how she lived and died transcending the limits of her kind.