Your best bet is to use the flash-scan method, then you can run the projector at normal speed.

Basically design an LED pulse circuit, replace the projector light with the LED source.

You 'flash' the LED light source 24 times per second, remove the shutter completely from the projector.

A hall effect sensor on the shaft of the projector will act as the trigger for the light source and the camera.

An enlarger lens reversed is the best quality lens for this sort of work, and is easy to adapt to the task.