Any reason a belt with holes couldn't replace the disk with holes for a more compact and rectangular viewing surface? Should be easy enough to test with a belt sander.
The closest thing from the time was mirror drums but those don't sound too similar, and they had mirrors for some reason.
No reason I can see except a high-speed belt is substantially more mechanically complex than a spinning disk. But the funny shape is part of the charm imo.
I think that the issue is that the display relies on persistence of vision and it might be a little difficult to find the correct spacing and setup to properly replicate the effect.
It would be worth looking into for a project though!