Regardless of the shape of the earth, at ground level to chase the sun one full revolution you’d have to be traveling at approximately 1000 MPH for 24 hours. Doable for let’s say some hi-tech blimp I suppose. But now you have to do the same thing in just an hour and a half. On land, to make one full revolution in 90 minutes, you’d have to be going something like 16x faster, or around 16,000 MPH. Rise in altitude, farther to travel, more speed required. Let me know if my math is wrong.
Well, I am still researching this so I didn't want to prematurely mention it, but I suspect that there are multiple dirigibles. As they move around some can "go dark" and not be visible. The "space station" is not always visible. Even round-earthers agree that you can't see it in day time. Plus there is no need to fly the dirigibles on cloudy nights. So with only a few windows of opportunity (night time, clear skies, outside of a high-light metropolitan area) mixed with having the right equipment to even see the dirigible there are only a handful of people at any given time who can confirm its existence. This severely limits the times and places where the dirigible needs to appear and with multiple dirigibles the illusion can be easily achieved.
On top of all that, if anyone here were to get the proper equipment, go out into a desolate field on a clear night and look for the "space station" and fail to find it? You would 100% chalk it up to user error. Tell me you wouldn't.