Please excuse my ignorance - I am a digital film maker and have never worked with film, but aren't you reinventing the wheel?
Hasn't the problem been solved by projectors?
Otherwise the image would creep up or down the wall as the movie progressed.
So, why don't you just repeat their mechanics - with a digital mechanism instead of a mechanical one.
That link shows how an old school projector moves the film based on the holes, therefore every frame is always centred.
Instead of the purely mechanical process you could use two servos, one to insert a pin into the hole, and the other to move it along one or two holes distance exactly every time.
Once you have the amplitude of distance between the leading edge of each hole, the image should stay in the same place of every picture.
Or have I made some ignorant assumptions?
Ps - this is a great project, please keep up the great work, our global history and culture needs it.