I finally wrote the code for this, and it basically works, but I'm not sure whether to go any further with it.
It's using a Nipkow drum to mechanically scan a lightfield. The drum has 32 lines, and the panel behind it is 64x64. It allows multiple holes in front of the panel simultaneously, so it ends up around 24x24 rays per hole.
A flickery low res mess, almost incomprehensible when seen on video, and a stupid way to achieve the limited effect it does. So on brand at least.

I'd probably have more love for it if I went all in and mechanically scanned both ends of each ray - another, faster, drum inside the current shell.

OK, it actually works quite well now*. I added a diffuser, and moved the scene closer to the plane of the panel.
Still not sure I can get a process video out of it.