There are such things as sound absorbing acoustic panels. They are used
to alter the acoustic response of conference rooms etc. You could a
couple to a board of thin mdf and position it behind the piano. It
should provide more efficient sound damping than the cushions. You
could do a google search for suppliers. It may lso halp to have an
extra-thick rug under the piano. Ttheoretically, I suppose you could
also lightly stick acoutic panels to the interior of the bottom door, if
there is room.
Best regards,
David Boyce.