So I'm thinking, what would make this sound a lot less like Stereolab? And what I come up with is having it played exclusively on a whole bunch of acoustic guitars. And then I'm thinking, what would then make it sound even more like Stereolab than it did to begin with? And what I come up with is changing the time signature to something weirder. It's not very nuanced or anything, but I think it works well enough.
Along the way I did some preparatory experimentation with what kind of bass sound I could get without a bass. It didn't exactly work, but it created a kind of insane noise that has its own use.