If your willing to use a AC synchonous motor and even a pulley system, the errors may be tolerable. I did a similar thing, with a piece of film that had to be moved over a window and had a take-up real. Someone else derived the equation based on the need to change the # of revs as the reel increased in diameter.
It can also be done with a DC motor if dynamic braking is employed. That can be done with a simple relay. In the off mode, the relay shorts the motor. You can use two relays an have a Direction and a not enable signal.
You can also have the motor run continuously. I did this with a 555 timer, transformer and AC synchronous motor (essentially made a variable frequency drive) for telescope elapsed photography for someone too, Now you just need a way to trigger the camera in intervals and possibly stop the camera while the picture is being taken, but you may not need to.