So I've dreamed up an effect that I've never seen before and which works in theory, but, of course, the devil is in the details...
Imagine a music video:
1. Film the artist performing in regular time, let's say 24fps.
2. Project that 24fps performance at 240 fps onto something moving quickly... dancers, blowing smoke, shattering ice, flowing fabric, etc.
3. Film the interaction of the projection with the objects using a high-speed camera at a matching frame rate of 240fps..
4. Play back the finished shot at 24fps to produce a mix of realtime footage projected onto slow-motion objects.
If you let your imagination run freely for a bit, you can come up with all kinds of interesting "time blended" shots, where cigarette smoke blowing from a model's mouth reveals the singer's face, or where the guitar solo is stretched and wrapped across the slowly turning body of a dancer.
The reason I think I can get away without the intermittent mechanism in the projection is that the only shutter that really matters is the one in the high speed camera. Even if the film is moving continuously through the gate at 240fps, a fast enough shutter speed and frame rate in the highspeed camera would eliminate motion blur in the projected image just as it does any other moving object. Synchronizing the camera and the projector would be difficult (maybe even impossible?) but since this would be a very expressive technique anyways, it would be fine to see a bit of the gaps between frames, or even a "film roll" effect as the camera and projector go in and out of phase. A certain amount of trial and error would be in order.
Using a strobe in the projector would certainly do much to remove any remaining blur...