Love this idea, maybe a little too much. Chalk it up to my long-standing appreciation for the Persona series, maybe.
Zelnick himself would be a good fit for the Fool, as he is the Zero; infinite possibilities and potential, but no direction (at least to start out).
I see Slylandro as the Magician. With their acquisition of the probes, they have had infinite possibilities opened to them, but they are also naive in using their new freedom and power.
High Priestess is difficult. My best idea is the Utwig, with their emphasis on the secret knowledge and mystical powers of the Ultron, as well as their willingness to share that knowledge freely. Possibly also the Arilou, with their hidden secrets, though their unwillingness to share them makes them a looser fit.
Talana is a shoe-in for Empress. She embodies mothering, attraction, fertility, etc. to a T.
The Emperor could possibly be the Chenjesu, as the father figures and leaders of the old Alliance. It's not a great fit, though, and I can't think of a better one.
Hayes could be the Heirophant. He is primarily concerned with advising Zelnick, and has a wealth of knowledge about a variety of topics to do so. He has much experience, and a high social position to go along with it. Of course, those same traits could also be associated with the Emperor, but I think that's not as good a fit.
Amusingly, barring the obvious choice of Talana again (I think she's a better fit for Empress), Admiral ZEX goes well with the Lovers. Interpret that as you will.
The Yehat are a lock for the Chariot. They embody every trait of the arcana perfectly, both positive and negative (Conquest, honor, victory, inflexibility, pride, etc.)
Strength could be represented by the Chmmr. Besides their obvious external might, they also have great inner strength, patience, composure, and self-control, all aspects of the arcana.
As already mentioned, the Hermit is a good fit for the Chenjesu. Unfortunately, this conflicts with them as the Emperor, and I don't see any good alternatives for either.
Fortune could be represented by the Utwig Bomb. Discovery and acquisition of this artifact marks the turning point in the conflict of SC2, a stroke of luck that changes the fight from one of a struggle against impossible odds, to one with a chance of victory.
Justice could possibly be represented by the Melnorme. They express a desire to remain impartial in the conflict, selling their wares and information to anyone willing to pay, and attempt to remain objective in their discussions of events. However, they also seem to be interested in aiding Zelnick (seemingly offering him substantial discounts on their goods when compared to discussions with other races about the Melnorme), possibly seeking justice against the Ur-Quan for their narrow escape and loss of their homeworld when they were still knows as the Mael-Num.
I don't know why, but when I saw this topic, I immediately thought Kzer-Za = Hanged Man. They are so trapped by their own rituals and trauma that they embody the inability to act in a meaningful way, despite the misery they cause for others though their actions. Of course, the same inability to act could also be applied to the Utwig while the Ultron is still broken, or the Syreen before being galvanized to action by Zelnick and the Mycon egg cases.
The only choice for Death is the Kohr-Ah. They represent the end of all things, and possibly even the major transition aspect of the arcana (Perhaps you will be reincarnated as an Ur-Quan).
Temperance is best represented by the New Alliance itself (though good luck figuring out an image for that). Even moreso than the old Alliance, the New Alliance represents the coming together and harmony among opposites, and the balance and recovery of the entire sector.
Devil is probably best represented by the Druuge, as previously mentioned, as their obsession with material wealth and temptation to Zelnick to perform terrible deeds to acquire material goods are their defining characteristics.
The Tower could be represented by the Neo-Dnyarri. He is the embodiment of chaos, disruption, and ruin, at least of the Ur-Quan, and physically generates crises and uncomfortable experiences for both the Ur-Quan and Zelnick at different times.
As already mentioned, the Pkunk fit the Star arcana perfectly.
The Orz could correspond to the Moon. They are practically emblematic of lack of clarity, obfuscation, and confusion. Of course, the same could be said of the Mycon, though the Mycon lack the aspects of potential doubt, anxiety, and deception that come from the Orz when you look beyond the surface of their words.
Sun is probably best represented by the ZoqFotPik. As a whole, they are alomst always optimistic, cheerful, and enthusiastic about their role in the Alliance, despite all of the hardship that befalls them, and continually maintain an air of innocence through the whole ordeal.
Judgement should be represented by the destruction of the Sa-Matra. This event marks Zelnick and his allies passing judgement on the Ur-Quan, and redeeming the entire galaxy from the yoke of their tyranny. It marks a new beginning for all sentients.
The World is best represented by the Earth, as the slave shield is finally removed. This final event gives the entire journey meaning, and is the accomplishment sought since the story's beginning. It fulfills Zelnick's goal, and begins Humanity's new ascent toward prosperity once more.
Unfortunately, I'm rather unfamiliar with the meanings of the cards in the minor arcana, so I can't comment at this time. Hopefully the major arcana will suffice for now.