RE: Hard mount or soft mount the camera?
What sort of camera is it, can you vary the exposure? If so open up the aperture which will require a faster shutter speed for any given lighting/film combination. If you can't vary the exposure but the camera is fully automatic, use a faster film eg 400 asa instead of 100 asa. (Do all the prop balancing stuff anyway as it's good practice with or without a camera)