Even though a 35mm cinema projector is running at 24 fps, the shutter inside the projector interrupts the beam twice during projection of a single frame, giving you a pulse rate 48 exposures per second. This was done to minimize perceived flicker, so you have to take that into account.
I would try anything at 1/30th and below to integrate the two exposures. It would be tricky to get a good exposure at a higher rate, as you may get 1 full frame and then a partial exposure of the repeated frame.