The older Roundshot used 120 or 220 roll film, and had a slit arrangement for exposing the film. Lenses off some 35mm cameras could be used, like a few of the 28mm Nikon manual focus lenses. You could hold the camera in your hand by the grip below it, and when you pressed the shutter release, the camera rotated about axis to exposure a length of film across the slit. Shots were possible in several angular rotations, even 360º (full rotation).
Dead Link Removed
This link is to the 28-220, which is still available. There is a nice animation image on this page, which shows the camera turning. So what I think on your reflective cylinder idea is that the cylinder substitutes for rotation, though you still need to move the film, or somehow expose it (hard to imagine a shutter for that). Anyway, I use to know a photographer who only shot hotels and resorts, and had one of the older Roundshot cameras, which is why I mentioned it.
Ciao!
Gordon Moat Photography