I think that most of the work has been done already.  If that track
can be transferred to a Mylar or PVC strip (or maybe one made of spring
brass) and then joined into a continuous loop, it could be stored in
a series of zigzags inside a relatively compact space.  I'm thinking
of the way Thomas Edison stored film in his very first movie equipment
-- let me see if I can find that...  Ah:

https://en.wikipedia.org/wiki/Kinetoscope#/media/File:Kinetoscope.jpg 

Mark Kinsler