I would rather we try to broaden the scope of the Hybrid Affinities further than attempt to dilute their themes. Hybrid identity is not well explored and rather one-note. And then compound this with the fact that mechanically speaking, the hybrids have minimal impact.
One of the key problems with Hybrid Affinities as they stand is that they are a 50/50 combination of their parent Affinities. They are an afterthought instead of being a brand new perspective for dealing with the planet and human evolution. That's the same problem I have with the Puritanical Harmony you've described. It is comprised of Harmony's goal to integrate with the planet and Purity's goal of rejecting any form of transhumanism. There is no synthesis; a new direction to take. If we're going to have hybrids, they should be treated with the same depth and care as the three Core Affinities.
I would approach this from the opposite direction and try to combine this "alternate" views on hybrid with the original to broaden the existing scope:
[Ascendancy] Harmony + Purity
To me, this Affinity is the belief in human evolution through the combination of Alien and Human genomes; the synthesis of a superhuman lifeform. Ascendancy strives to improve humanity to its peak potential. Improving human biological function, while preserving and idolizing the human form. This take helps make it stand away from being Purity+ more genetic modification.
When interacting with the planet, I think they would still try to terraform the planet, but were Purity does it through brute force, H+P is about finesse. They would uplift organisms and modify environments but would be more gentle in their planetary interactions. In their eyes, humanity takes precedence over the planet, but not at the cost of depriving future generations.
[Mastery] Purity + Supremacy
it took me a long time to come to this conclusion, but I'm happy with the definition I came up with for this Affinity. Mastery is the ethos of the primacy of human life supported by the fruits of human labor. Unlike Supremacists, followers of this Affinity integrate technology into society, rather than directly into humanity itself. As such, Mastery uses its expertise in technology to protect and foster human prosperity. Drawing strength from the connections and synthesis of machine with society. Yes, this hybrid cares about subservient machines. I would say cognitive androids with limitations would increase as society progressed. Whether or not they're considered "alive" and how they're treated can vary depending on perspective. But I am convinced that they're the most likely to shape machines in the IMAGE of humanity. Whereas Supremacy doesn't draw that line anywhere and Purity stops at "Dumb AI" for support systems.
I would imagine that this hybrid would be most likely to shut itself away from the world. Preferring to live in Domed Cities (likely Hermetic) and acting through remote controlled drone proxies.
[Voracity] Supremacy + Harmony
It took me forever to change my perspective on this hybrid. It's FAR to easy to paint them as the unethical transhumanists. While this Affinity is about improving humanity by any means necessary, applying radical transformations to human physiology and psychology via alien or technological augmentation; this hybrid is also about diversity, innovation, and adaptation. They make the most of everything and strive toward being the best with what they have available.
I imagine there is a place and function for everyone; humans, cyborgs, alien hybrids, synthetic lifeforms. The only caveat is that they reject the history and nostalgia that Purity celebrates. Their eyes on on building a better future, starting today.
Being as adaptive as they are, I see this Affinity finding new ways to deal with terrain that other humans would probably try to avoid. Swamps, Deserts, Tundra; these are just new opportunities to explore. They would make the most of their land, finding new ways to live.
And as sci-fi loving architect in training I am, I picture their cities operating as living organisms. Biomechanical infrastructure, living building envelopes, artificial ecological features, machine accelerated natural processes like fluid and particulate filtration, etc. Their cities would be built to be compatible with their climate and ecosystem, with some technical armatures to help optimize processes.