Jere,  Ed Schmidt has a good selection of recut 14-note, 7-3/4"
music strips suitable for play on such instruments.  See:

  http://www.music-rolls.com/index.php?page=Catalog 

As there were several companies originally supplying this size
music, as seen by the variety of stamps on the music you've
encountered, it was as close to a "standard" as you can get in
organettes.  But your "Organita" is a less-than-common instrument.
The "strip" music you have was evidently rolled up for storage.

Todd Augsburger - Roller Organs
http://www.rollerorgans.com/