I don't think the site below is the originator of this hack, but it's where I found the image. I remember seeing the record player a while back and thinking that's pretty simple - it's just a motor. But after seeing the film projector, my appreciation has grown.
True, it's just about finding the correct gearing, but the use of a paper cone to amplify the sound is a nice, low-tech, touch which fits in with the rest of the model. Maybe there's scope in an alternate design whereby an elastic band drives the turntable to give it a true 'wind-up gramophone' vibe.