The photos below show my experimental set-up. It's simply a gutted projector with a slower motor and a cooler LED lamp.  The lamp still gets hot, so is cooled by a fan.  Its wide beam is also masked off by a piece of foil.  A smaller LED would probably be a much better solution, but I'm using what I had available.

There's a book propped up as a screen and a gorillapod stand for my camera-phone to photograph the frames as they go by.

I'd like to mount this in a more solid manner, with some enclosure around the screen so I can operate the system in the daytime.  The fan needs to be moved to allow for a bigger take-up spool and I need to be able to plug in a power cable for my 'phone whilst capturing - at the moment the USB socket rests on the table.  Other additions would include a shutter release switch to synchronise the projector and camera and some way (VNC, miracast?) of viewing the screen remotely.