I have had success with the removal of minor dents with the steam
method.  I have only done this after the finish was removed, so I don't
know how useful this will be for a piano with the finish in tact.

If the wood fibers are not broken, the application of gentle wet heat
will cause them to relax and return to nearly the original condition.
Dents that have gone as far as the cross-banding can be nearly leveled.
Just use a damp (not wet) cloth and apply heat with a warm to hot iron.

The water will raise the grain of the wood and sanding will be
necessary.  The moisture will probably not penetrate a varnish or
lacquer finish.  It will have to be removed.  It will probably ruin the
finish if it does penetrate.  Once you get the dent out, you will have
the problem of matching the old finish.  This might be more difficult
and even more unsightly, if done badly, than the original dent.

Spencer Chase