I can verify that many of these old finishes are shellac.  Take some
alcohol on a cloth and touch it somewhere not too visible.  If it gets
sticky, it's shellac.  (It's a good idea to try on a small unseen area.)

I have been learning to restore them.  You don't need to strip them if
you like the color.  Not stripping is a big advantage because the grain
filler and stain do not have to be redone.

Spray a nice liquid coat of clear shellac over the top and see what
happens.  I find it often knits the alligatoring together.  Four or
five coats, sand it flat, another three or four coats, sand it flat
again, then spray a final coat.  Dewaxed shellac seems to work better
and harden up more quickly.  I have been using matte nitrocellulose
lacquer over the shellac and getting beautiful results.  Looks hand
rubbed.

On an upright you can test the finish inside of the lid or the top of
the nameboard.  On a grand the inside of a leg or the back of the pedal
lyre is a good test surface.

I am doing a Marshal & Wendell grand that had severe water damage on
the lid.  Many areas that looked awful improved dramatically with just
one coat.  Shellac dissolves the layer underneath and knits together
into a unitized finish.  Can look terrible right after spraying, but it
flattens out and becomes sandable as the coats go on.

I don't know about the durability; will it craze again?  Has anybody
else tried this?

Joseph Osborne
Carlisle, Pennsylvania
http://www.osbornej.com/