Found it! Or more precisely, found them. My good friend, George Epple,
suggested that Larry Givens' book, "Re-Enacting the Artist," might
contain the information I was seeking about Ampico's use of an
automatic machine in the factory for setting unit valves as a function
of the valve's volumetric flow parameter instead of the more traditional
way, practiced by essentially all modern-day restorers of setting the
distance the valve poppet travels. 

In many, if not most cases, very satisfactory results will be obtained
by this method if the restorer is careful to use consistent methods and
materials when rebuilding the valves, but I digress. For those wishing
to gild the lily, further instruction is, well, instructive.

George's suggestion was most helpful but required a bit of research.
Givens notes on page 66 that an employee of the American Piano Company
by the name of Boyd Dudley, Jr., "devised" the method that resulted in
the automatic adjustment machine. 

Dudley is a name probably unknown to all but the most dedicated student
of the genre. Certainly, it was (unknown) to me. I would have surmised
that an invention of this utility and sophistication would have been
squarely in Hickman's wheelhouse. Givens make no suggestion as to
Dudley's motivation; it could well be Hickman conceived the idea and
tapped Dudley, an obviously skilled fellow, to make it happen.

Dudley came up with not one, but two patents that document the device.
Both were filed on the same day, July 10, 1924, and issued the same day,
Sept. 11, 1928, with consecutive patent numbers.

The first, #1,684,014, is the simpler of the two, and is more conceptual
in nature, appearing to show a non-automated device and method whereby
a technician could manually operate a valve cover "ramming" device
in response to visually monitoring a manometer-like device that is
calibrated using a "standard/reference" valve for its volumetric flow
parameter. The companion patent, #1,684,015, is much more detailed
(11 pages vs. 3 pages for the first patent) and describes the fully
automated factory device. 

Neither Givens nor any other reference of which I am aware represent
that the factory device was unique, indeed, line 9 of page 2 presents
the conjecture that two of the machines could be used alternately by
a single operator, presumably loading one machine with a valve to be
calibrated, while the second machine is actively performing the
adjustment on the valve currently loaded into it.

No mention is made of a "cycle time", but I would imagine that the
limiting factor would be how fast the operator could make the switch.
My guess is that a skilled operator could possibly calibrate upwards
of 8 to 10 valves per minute. Prudence would dictate having a third
machine in "ready reserve" in case of a debilitating malfunction of
one of the active machines. 

I am curious about this (these) machine(s) and the process in order to
optimize my design for a similar purpose device which would be available
to those who would care to speed up (or at least improve the accuracy
of) the calibration process of unit valves, specifically Ampico/Amphion
types, but possibly adaptable to other brands such as Simplex,
Gulbranson and WurliTzer. Granted, it will require substituting custom
designed covers for the metal ones, or in the case of earlier valves,
the wooden ones; however, in my view, this is "worth it" to achieve
greater note-to-note consistency. 

Finally, this fresh re-reading of portions of Givens (pp. 52 and 58)
reaffirmed my previously stated conjecture (here and in other fora)
that the vastly reduced operation speed of the Model "B" expression
regulators required the tracker bar holes for the stepped intensity
functions (2B, 4B, 6B, 7B, 7T, 6T, 4T, 2T) needed to be positionally
"retarded" on the tracker bar in order to provide compatibility with
 earlier coded "A" rolls.

Givens gives the amount of this offset as one-thirty-second of an
inch (1/32"), but cites no evidence of either this dimension or the
definitive purpose of the offset, such as statements by Dr. Hickman
or reference to his journal writings. I am aware there are differing
opinions about this subject. (See a more thorough discussion at

https://www.facebook.com/groups/playerpianotalk/permalink/10156199528225831/ 

John Grant