I finally made it out by doing an entire run of the foundry and using the option at the end to go to the fleet instead.
After taking a break, I went back to Quesh. I can now see that there is no floor to the spacestation. I'm safe as long as I stay in my story area but on the other side of the barrier, there is no floor
This is a class mission, so I guess I'm not able to continue playing this guy until they get it fixed. I'll try a few more things, but this sucks.