I'm so frustrated with the Dark Wheel I tried the last thing I could think of...
...I started murdering every last one of them. I went to Shinrarta Dezhra and the one other system they were in and I torpedoed their bases, abandoned their missions, and hunted down and murdered as many of their ships as I could. I'm hated by them now. Took me a few days to reduce my notoriety back to zero. Best working theory I had was that if they weren't the true Dark Wheel then hunting them was what the true Dark Wheel would do, and that would get me noticed by the true Dark Wheel.
And I'm not one clue closer to finding the station. Was really hoping it'd be a Ready Player Moment of "I wish we could go backwards, really fast." I mean, Bill and Ted did it...