This looks like a lot of fun and I can imagine that playing it at a group with my tabletop people, it'd be a LOT of chaotic hijinks. I like that your addenda suggests ways to skin it into existing RPGS - I raise you one further, I feel like it could probably also be tweaked to fit into non-space-themed games, if the GM was able to come up with a parallel high-stakes scenario that required characters to interact with it for a "fix" in this timed way. Like, a protective warding spell cast on an object that your party is trying to steal, or grabbing onto steady things when sinking into quicksand.
I wanted to share the feedback that I had some trouble parsing how to use each of the cores; I think your mechanics are really cool and interesting, but I had to reread through the simple instructions a few times to try to work out how exactly players were meant to interact with their dice, the core dice in the middle, and the rules of their specific consoles. I'd be curious to see if there was a little bit more instruction you could add that would clarify for a potential group of players. For example, "Roll a d6 and add it to the Multiplicator." What's the Multiplicator? Is it the core? Is it a pool of dice you have going at your own console?
To be clear, I like this premise a great deal, I think it's probably just that I'm missing out on something that feels clear in your head. I sat with a pile of d6 and did some sample rolls, and I think I connected the dots okay enough to see how it'd play out but I'm not sure, and that's where I start to wonder if something could be clearer. I think that's the most challenging part of instructional design - navigating the space between your mechanics and the starting-point of someone who has never played the game before. I hope this feedback makes sense, I can try to explain it further if you have a question about it!
Anyway, thanks for reading this rambling feedback! And thanks for making this really fun and flexible mini-game!