In discussing the topic of saving the original piano (or any other
piece of furniture) finish, David Dewey references a "re-amalgamator".
I have for years used Homer Formby's Furniture Refinisher which does
exactly what he describes.

I had a piano some years ago which had been covered almost all over
with contact paper and then left for many years on an unheated porch.
I was able to remove mechanically, all of the contact paper and then
used a stripper to remove any remaining glue from the surface.  Most
of the original stain and finish remained although somewhat marred and
very dull with hints of alligatoring.

The Formby's Refinisher essentially smoothed out all the irregularities
and spread the original finish around so that it was quite homogenous.
This process lightened the finish quite a bit and brought the overall
color back to what it probably was when new.  I then finished the piano
with Formby's wiping tung oil finish which brought out the glossy
appearance.

I was able to save the fallboard decal by very carefully working the
refinisher around it leaving an oval with the decal in the center.  The
final effect of all this was a piano that, while not looking like a
French polish, nonetheless looks very professionally done.  I just
checked and Formby's has a website so they are still around.  I used to
get it at a local hardware store or Home Depot but haven't looked for
it for several years.

Bob Conant