Giving it some thought, even if you didn't try to incorporate Alien: Earth wholesale with a timeline tweak, there are actually things that could easily be mined for rpg campaigns if you shift the context a little:
- The C-Class Deep Space Explorer / Science Vessel and the apparent crew composition of science, security and engineers (with a lower case "e"

). This will be easier to create after Episode 5 I think.
- The other dangerous invasive lifeforms (once we see more of their capabilities.)
If you keep the Hybrid program you could pretty much create them by using a Synthetic with the Kid career, but since they have (augmented) human minds, they need to have the Stress mechanic applied to them. Wendy is a bit of an odd-one out (and some of that is down to the fact that she's trying to protect her brother, and she seems to have certain heightened senses, possibly her hearing) but the others are standard kids in synth bodies, and we're told they have super-computers augmenting their brains, although only Curly and Toodles (and arguably, Wendy) are demonstrating this.
Maybe let them Push rolls, but double the Stress cost? When they're not freaking out its probably more to do with naivety than mental fortitude....
You could also pretty much keep Prodigy as is, an upcoming player on the corporate stage with major holdings in Thailand. Of course, if you're playing the game in 2183, maybe see where Prodigy stands by the end of the series. (And I suspect it won't be in a good place....)
I probably wouldn't add Morrow's tech myself. I'm okay with cyborgs in the implants or limb augmentation area, but these don't seem to be a big part of the setting, its more of a Predator thing I think. Augments tend to be exo-skeleton type stuff rather than taking a more Cyberpunk approach, although Blue's neural implant in "The Cold Forge " is an outlyer here. I'd also assume that the "real-world" physical limitations of using cybernetics would apply - you can give me an arm with enhanced strength but the rest of my body that its attached to has to be able to support that, or it'll tear itself off when I try to lift that truck....
I guess ( if we ignore neural links and implanted gadgets for the moment) you could treat cybernetics as an extension of Attributes and the Push mechanic. They add +1 to the Dice Pool of skill tests based on the attribute being enhanced, and you can Push twice (with the standard Stress cost)?
I can see the case for hybrids to have access to the stress mechanic. They ought to be subject to it because they still have human reactions, or at least are designed to simulate human reactions. IMO, the original children were killed, not "transferred". But anyway, it's a solid case to say that they should get frightened, maybe even panic. Wendy says that her emotions are "quiet now" and the scientists say that's because she lacks adrenaline, etc. Depending on how closely you want to stick to what you see in the show, it would make sense to have a greater resistance to stress. You could have an alternate table though much simpler to reflect it like a talent with an inherent -2 to the Panic result or something. Conversely you'd probably also want them to not gain as much benefit. Frankly, it's a bit of an uncomfortable middle-ground that you'd implement with something like "ignore the first three points of stress" which would reflect the descriptions in the show but be ugly as a mechanic. Also worth mentioning that whilst Wendy and the others are children PCs in the game would not necessarily be so and would be much more comfortable in their robustness. The children are still recently copied into the bodies and still acting like they're fragile (Wendy excepted). Jumping at dead cats or backing away from blood-sucking leeches even though they don't have real blood. An adult in the body, especially if grown used to it, is going to start losing such legacy instincts. There's only so many times you jump from a 100m cliff before you stop being afraid of 100m cliffs. All in all, they pretty much have to suffer less from stress to be believable. They're not going to drown, probably not going to suffocate. Hell for all we know they might even be able to back up their minds given a few more years of technology. It's only 2120 in this timeline.
What do you do with the stress mechanic when even though not immune like androids, it's got to be so different to humans? I think closely related to this is the question of balance and their capabilities. If we're talking the superhuman ones in the show that can solo melee a grown xenomorph. And again, Wendy is a child presumably without combat training, certainly no combat experience and likely not optimised for combat the way one could be, that's a massive jump compared to other PCs and synthetics. I'd say if implementing in the game you have two choices - it's either reserved for special NPCs or you have toned down models that are more routine. I'd honestly be inclined to go with the former given the fiddliness of stress for synthetics at the same time. Really the two issues are closely related - the more super the model is, the less it should logically be subject to panic. The less super, the more it might genuinely feel fear. Though there's still the issue that it's a simulation in many ways - the scientists say they can dial its emotionality up and down. Which is pretty concerning if you're trying to convince yourself you're actually the original person.
It's a little bit of a cop-out but if I wanted to introduce that sort of transhumanism into the gameline I'd lean more towards it being an NPC. If a player had a real concept for a hybrid that they wanted to play that couldn't be satisfied by playing an android, I'd actually be more inclined to go the Morrow route as I see that as closer to the canon setting in some ways and the player is still human and has human stress (though could have implants to affect it). If having an actual PC hybrid... probably inherently have a talent that helps resist panic, easily done. But I'm still stuck with someone who has Android level abilities but less of the balancing limitations. And though it's unspoken a common trope in Alien - which my impression is that it's more often played as Cinematics than Campaigns - is that the android is not always trustworthy. Nor are people to be fair but androids also usually have some strict programming. Like being incapable of harming a human for example. It's no one thing it's just that androids come with a whole lot of baggage in the setting not all of which applies to a hybrid who really is the best of both.
I don't know - bit of an off-the-cuff rambling answer. Your ideas of how to do them by basing them on synthetics and doubling the stress seems viable to me. I just wouldn't intrinsically tie it to the Kid career unless you're specifically building the kids from the show. Also, the kid's talents are based around his size which no longer applies here. With their super brains there's no reason one couldn't be a scientist or marine (though not in name) even if the personality were childlike.
I just feel that for something with transhumanist themes I lean towards a system more designed for deeper mechanics and long-term development. The old Eclipse Phase RPG was a transhumanist RPG that would handle a lot of this stuff with much more granularity that fits customisation and body swapping and such.
Don't know if any of that is helpful or not (probably not

). I was thinking as I typed based on your post.
Also, the Maginot seems strangely large for a C-Class, or is it just me?