We had a similar problem and solved it by accident.  While building
a recording studio in our home, we had limited area for storage for
the building materials.  Much of the bulk was in sound proofing.
These materials were temporarily stored beneath our Knabe Pianocorder.

When we played the piano at normal volume with the top closed, it was
a very pleasant volume for easy listening.  When the sound proofing
materials were finally installed in the music studio, the piano was
back to its brilliant concert shell volume.

Making a long story short, the materials we used were ThermaFiber
Mineral wool sound attenuation blanket (Thermafiber Inc., Wabash, IN
46922) and Johns Manville Insul-shield, plain facing.  These are ridged
bats usually used for fabricating cloth covered sound dampening panels
for use in recording studios and in acoustical clouds (Johns Manville
Insulations, Denver, CO 90217).  We ordered these materials off the
Internet.

The sound attenuation blanket bats are much like garden-variety
fiberglass insulation but is designed to dampen sound, and it does
an excellent job.  It can be pulled apart and loosely stuffed into
pillowcases then inserted behind the piano against the sounding board
and wall.  This stuff is really horrible to work with -- gloves and
breathing mask a must, and try to stay upwind.  Be prepared to itch
for a while.

The rigid insulation can be used inside the piano to dampen, if desired;
I would use as many bats as possible without infringing on any moving
parts.  It is very easy to cut with a utility knife.  It is best to use
spray glue and cover the bats with scrim cloth to mitigate any fiberglass
sloughing off and getting into the players vacuum system.

The soft pedal rail can be permanently adjusted to a soft state, if
that has not already been done, and the player vacuum can be adjusted
to the lowest setting that still will play all the notes.  Nothing is
worse than only part of a song playing because of dropped notes.  But
I'm preaching to the choir!

Best of luck, I hope this does the trick or at least helps.

Tim L'Amoureux
timlamour@aol.com.geentroep [delete ".geentroep" to reply]