Dear Dr. Passen:  There are several steps needed to determine why any
pipe is not speaking.  I have not personally worked on the brand of
calliope you have but as a pipe organ technician there are commonalties
involved between a calliope whistle and an organ pipe.  The following
then are steps toward resolving your dilemma.

1) Have you checked the wind pressure to be sure it is up and correct?
The use of a wind gauge to determine correct pressure is always the
first step.  If factory specs are available, be sure the wind pressure
is set to them.

2) Do your pipes have tuning stoppers?  If they have become leaky in
the restoration process, the pipes cannot build up a standing wave for
oscillation/speech.  Even a pinhole is detrimental to operation.

3) The cutup, height of the mouth opening, is somewhat critical.  Were
the pipes disassembled then reassembled with the wrong distances caused
by spacers being used from other pipes in the set?  Each pipe is unique
and if the brass restorer didn't keep all the parts for each pipe as a
unit there can be problems.  Tangley's and others use permanently
soldered connections that cannot be easily altered.

4) The direction of the windsheet (air jet) coming out of the base
windway slit is determined by the setting of the languid, the round
plug across the mouth lower lip bottom on a calliope pipe.  The languid
must direct the windsheet to impinge very precisely on the upper lip at
the bottom of the resonator.  The placement of the air jet is the most
critical adjustment in voicing any flue pipe.

5) There must be no leftover hardened polish or other material in any
part of the windway.  Any impediment to the clean flow of air in an even
laminar fashion will cause voicing problems.

As for your inquiry about how a pipe speaks, the physics is actually
quite complicated and books have been written about aeolian tone
generation.  At the most basic explanation, it can be said that a jet
of air leaves a constricting orifice as a laminar sheet but quickly
begins to slow and create a meandering oscillation such that when
striking a dividing wedge pulsations of the opposing vortices produce
a standing wave within a resonator body.  The fluid dynamics and
attendant calculations are somewhat lengthy.

Your assumption about the fluidic mechanism applying to wind exciting
the calliope pipe being the same as your blowing across the mouth of a
soda bottle to make a tone is not correct.  A soda bottle is an example
of a Helmholtz oscillator whereas an organ pipe is a traveling wave
oscillator.  The excitation mechanisms are different as is the resonant
frequency determination.  However, both do take some practice to get
the flow dynamics correct for oscillation.

Kindest wishes,
Albert F. Sefl, Ph.D. - retired physicist and organ tinkerer...

P.S. If you were local to the San Francisco area I would make a free
house call.  Diagnosing a pipe speech problem is always easier in person.