Andy, your "discovery", the Mechanical Orguinette, is indeed
restorable and will make a nice addition to your collection.
Recut music 14-note, 7-3/4", is readily available from Ed Schmidt,
see a catalog at http://www.music-rolls.com/  Normal rebuilding
practices will work, and if you don't have suitable cloth and glue
it may be obtained from http://www.leathersupplyhouse.com/ or myself.

A replacement rubber drive roller can be made from rubber tubing
(latex or similar, such as from http://www.mcmaster.com/), and can
be lubricated with soapy water and slid onto the shaft.  The "relief
valve" you mention is made to open as the reservoir is drawn fully
closed, so that the vacuum does not become too great and damage the
bellows.

I'm not sure about a source for the missing spring, but you might
try restorer Harold Draper <draperz@msn.com> to see if he has a spare.
You are correct that similar models were available with or without
spools: strips or short rolls could be easily played without spools,
or longer multi-tune rolls and rolls made up from connected strips
conveniently played from the spools.  The 14-note music was probably
a very popular size, so you might also find some original music for
display.

These are sturdy machines, intended to be used, so I'm sure you'll
enjoy it.  But watch out -- you might be tempted to start collecting
organettes!

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