Species X is unique in several ways.
They were (the history lost to their people) genetically engineered originally, and appear as hairless humans of (intentionally) non-human looking skin of various grays, blues, and purples. They cannot reproduce, and depend on growing new members of their species artificially in a process similar to cloning (through combining multiple genetic bases in a way that leaves members being genetic copies nearly statistically impossible). Their species can be engineered to exaggerate some aspects at the costs of others; certain areas of the brain could be stimulated at the risk of mental deficiencies in others, or muscular growth could be set on the genetic level and sacrificing some other aspect. The most healthy (mentally and physically) members of their species tend to be the ones who are not guided genetically. Thus this allows them to somewhat create specialists, but not a 'master race.' Baseline they're roughly comparable to humans, but have shorter lifespans by a couple of decades. Growing a member of the species takes 2-3 years, and once the member emerges they do so with the reasoning, motor skills, and speech capabilities associated with early grade school, and are physically similar to humans in their early 20s. They lack reproductive organs, and do not look distinctly male or female.
The facilities that grow them have fallen into disrepair, and knowledge sharing about the growing process is almost non existent. The process of growing and modifying the genetics has devolved into superstition, and baring an academic revolution no meaningful advancement of the field will be seen. In fact, any attempts to make new facilities have ended in disaster, and this too has worked its way into their abstract superstition. Individuals have been flogged and hung who suggested tampering with the facilities to improve them.
Species X is also unique mentally from humans; they lack humanity's biological drive for tribalism and are biologically distrusting of others. They are very defensive (very wary of threats and find it difficult to form relations of trust), and readily separate and distance themselves. They do, however, biologically value recognition of others more than humans, and very much respond to a desire for a sense of power or authority.
Those who control the growing facilities control the power, but due to the nature of the species/culture, those who control the facilities aren't promised to remain in power long before an inevitable overthrow is attempted.
This mental biology would drive them to disperse, except the other species of the galaxy are extremely racist towards them, viewing them as a thieving, warlike culture (a reputation they have somewhat earned). Most organized groups of the galaxy are only a stone's throw away from endorsing their genocide.
To avoid extermination, they realize the need to band together, even if they are biologically repulsed by the idea. They need to come together and craft a government that:
- The facility owners can agree upon, and will support
- Will endure change of power of the facility owners
- Will endure the general lack of trust and strong sense of individualism of the species
- Will allow them to mass a military quickly if a threat arises
- Will resist internal forces that might attempt to tear it apart
- Will provide a unified movement to direct them in war
- Will show the external galaxy that they are a unified force
To clarify: the primary reason for the government is simple survival, not embetterment of the species, or trade, etc, although they would probably welcome that. Further, the government isn't attempting to achieve a moral highground; the growing facility owners are fine with forming a government under force if need be.
What government would support Species X, and best achieve these goals?
Additional Information Per Request(s)
There's around 100 facilities scattered around a single planet on the various continents of the planet. The facilities vary in size, with about a dozen or so being clearly the largest.
The current leadership of the facilities tend to have acquired their power through coercing others (including, but certainly not limited to violence) or making deals. Others might have used industries they lead, or simple wealth to provide leverage to make their way on top.
Power than is typically maintained since in <8 years those commanding the facility can begin to produce members of their species who are indoctrinated (as best as they can be) for loyalty. This isn't a guarantee by any means, however.
Lacking the draw of tribalism has significantly impacted their record keeping as they don't see the value of preserving the history of their ancestors. However as best as they know they escaped their masters 1000 - 3000 years ago (a period that, during which, they rediscovered a variety of technologies including spaceflight and later intersystem travel).
The facilities have undergone a process over those years similar to ship of Theseus; none of their parts are original, but they still serve (after a fashion) the original purpose. Slowly, crudely, they're repaired and parts are replaced to keep them functioning.