First, I'd have to doubt that 20th century pianos are finished in
oil varnishes; I think they're lacquer.  I think the stains are
lacquer-based as well.  A few moments with a rag and lacquer thinner
will demonstrate.  Lacquer dries much more quickly and is amenable
to a rubbed finish while varnishes have a surface film which is not.

Secondly, try marine varnishes.  They're still available.
Additionally, varnish can be home brewed; it's basically boiled
linseed oil and dryers.

More than you might wish to know: http://en.wikipedia.org/wiki/Varnish 
Interestingly, they think that all clear finishes are varnish.

Douglas S. Heckrotte
Philadelphia, Pennsylvania