Have you tested making "loops" with larger frame counts by example printing out a strip and taping the ends together and spinning it to create a movie effect? Does that make sense?
This wouldn't work smoothly because each image would be, for example, 2 inches wide. You may have several frames per image, but then your eyes would have to jump two inches to the next frame. The old style zoetrope would have a much cleaner effect.
That's actually one reason why we're limiting things to up/down rotation also — the spacing of your eyes makes it hard to display lots of frames accurately when you're rotating it left/right. And zoetropes, so cool! We really want to try some of these out too: http://www.thisiscolossal.com/2013/10/the-first-animated-gif...
You could have four of these (maybe more?) with the top edges glued to a stick (side view: +). As you rotate the stick, you'd see 10 frames per sheet, then focus on the next one. I'm not sure if that would work.