I think Robbie has the answer.  Very hard hammers (a drop of lacquer?)
combined with one string out of unison a bit on every note (well,
maybe not even every note!) would probably bring you that "magic" you
seek.  If the bass would be a bit flatter than the mid range, and the
high treble a bit flat to the mid range, I would think it would closely
approximate a neglected piano.  But hey, it's just an idea!

David Dewey