Sounds like a fun project! I did some quick searching around for a portable 35mm projector because I swore Kodak used to make one, but all I found was the Pageant 16mm version.
The most difficult part will be the intermittent motion. Perhaps you could buy a gate on eBay that includes the gear train for that?
You could use the optics from a slide projector and maybe even the light bulb setup too.
It actually sounds like a pretty difficult project to me, but I’m hoping you keep at it so we can see what you come up with!