I wish I could chime in with factual data.  However some of the
question of valve response was addressed in organ technical literature.
As a kid I found in the Portland Oregon main library (the one with the
nude statue of Venus in the lobby) a book that described pouch size,
tube size and length.  There were many long math formulas.

After I acquired my first player I went back as an adult some 20 years
later and looked for the book. I was never able to find it.  Aside, the
tubular pneumatic action I observed and played has much larger tubes
than used in players.

Furthering my search I went through everything pneumatic at the
University Of Washington libraries.  There a book in Russian described
in detail the pneumatic motor and other controls.

In my searches I found that the Russians had a pneumatic calculator at
the turn of the last century.  I could find no further info on it, but
it would be interesting to explore.

A 1980s organ builders journal published an extensive analysis of valve
speeds of various actions, including tubular pneumatic.  I have the
issue put away, somewhere, somewhere.

Speaking of mass in the tubes, how much of a factor is humidity --
little, I suspect.

Bill Chapman
in La Quinta, California, with desert temp of 83 F.

 [ Weather conditions at Palm Springs Regional Airport, reported at
 [ about 2 PM today, were 84 degrees F. and 12% relative humidity.
 [ How're your player pianos doing, Bill?  ;-)  -- Robbie