I was wrong about the shutter, I'm used to dealing with a different system of professional equipment.
Most projectors and cine/movie cameras have a revolving shutter, with appox. a 170/175 degree cut out.
It would seem the standard revolving shutter has two opposite cutouts of approx. 85 degrees, to improve out of balance
forces and cut down vibration. The shutter runs at half speed. I apologize for my error.
It is quite probable that what you are suggesting will work fine with B/W film. With low light, just run slower.
The only problems left I think, will be to get an even illumination across the frame. You may need a field lens in the light path
to collect enough light. The other problem will be to get the camera to pickup the projected image. One way is an aerial
image system (my previous post mentions this). You could also try a semi-translucent screen between the projector and
the Pi camera. Its going to need a bit of experimenting. I wish you luck.