So, as I said, here is a video of moving reel. This is just a simple stepper motor taken from a printer or scanner - I don't remember. Reel band does not match Dam Buster. It is taken from Andy Capp game, but it doesn't matter in this example.
The main thing I'd like to show, is that it works. It is possible and it is confirmed.
Reel movement works. Reel shaking works. Directions of movement works. Nudging works.
I'm not quite satisfied with accuracy, because sometimes reel makes longer spin. Most of the time it lands on propper spot, but sometimes it skips steps. Arduino serial transmission is a problem here. I will have to work it out. For now it is just a firework feature. After I will get 100% accuracy it will be added to my program. And here is the video: