Use of a digital camera and projector, as you've suggested, is probably the simplest way. I would only suggest that, instead of a projecting onto a screen or wall, you use a video transfer device such as those designed originally for transferring movies-to-tape.
These devices have two openings and an internal mirror at a 45 degree angle. The projector plays into one opening, and your video camera records at the other opening.
The resulting quality will be much better than if projected/recorded off a wall or screen.
They should be cheap, and even be available on ebay .