Thanks to John Grant and Craig Brougher and all for the lively
discussions and a review of basic physics.  Indeed, there are many
factors in the player piano which will affect the sound intensity.
I'm still compiling a list of all that can happen:

1.  The air exhausting from the pneumatic may become turbulent,
which reduces the flow rate and hence the rate-of-change of the vacuum
within the pneumatic.

2.  The force exerted by the striker pneumatic upon the key diminishes
as the pneumatic closes -- the force is non-linear.

3.  The hammer mechanism (a la Cristofori) multiplies the motion of the
key, but this motion-transfer-function is also non-linear.

4.  Reducing the hammer travel distance by lifting the hammer rest
rail results in the striker pneumatic operating over a reduced span
where it is mostly closed, therefore less force.  Simultaneously, the
hammer mechanism is operating at reduced span, where the mechanical
multiplication is less -- it's also non-linear.

All these idiosyncrasies could be reduced to tidy equations, or failing
that, plotted on graph paper.  Certainly Dr. Hickman investigated many
of these problems at the Ampico Laboratory; he wrote equations of
physics and also made machines to measure what actually happens inside
the player and piano mechanisms.

The analysis of the physics and mathematics is just to make sure we
don't overlook some important subtlety.  Most important, the researcher
who has prepared himself by studying the theory is much more likely
to gather experimental data of good value.  He is not likely to dismiss
an unusual data measurement as "random noise" -- he will search for
cause.  If the unusual data is really noise, then he improves the
experiment setup.  Otherwise he will pursue an explanation.

The real world of engineering must balance theoretical efforts (time and
money) with empirical methods, in order to solve a practical problem in
a reasonable time.   So, the next step is to rig up a microphone and
oscilloscope at the piano, and gather quantitative data about the
relationship of stack pressure to sound intensity for use in the overall
transfer functions of the reproducing piano system.  It really doesn't
matter much what happens in the path between the pneumatic and the
sound, as long as the overall transfer-function is reasonably accurate.

In other words, at some point in the project, measuring the real-world
actions is better than belaboring the theory.

In still other words (growled by a few former bosses I worked under):

"Shoot the engineer and get on with it!"

-- Robbie Rhodes