Hi.   I'm new to the group and have finished about 4 pianos so far.
The first 3 pianos I stripped the old finish off using standard paint
stripper, sanded the finish, stained it, and sprayed on a good quality
lacquer (multiple coats with light sanding between each coat).  These
pianos looked fine but didn't have a glass like finish.  Small
crevasses formed on the top of finish because of the pores in the
wood.  These can be eliminated by more sanding and more painting.

The 4th piano I used a Paste Wood filler before applying the finish.
This provided a smooth surface for the Lacquer to be sprayed on which
created a glasslike finish when it was finished.   I used a Behlen
(Pore-O-Pac) Paste Wood Filler that also included a stain.

To apply the filler, you simply paint in on with a brush, wait 2-5
minutes for the paste to harden slightly and then scrap the excess off
using a putty knife or plastic card.  One mistake that I did was to
just wipe the putty off and leave some of it on the wood to be sanded
off later.  This didn't work!  Sanding didn't remove the sealer but
just deposited a very thin layer over the wood which hid the wood
grain.  I had to remove the Paste down to the wood using a Naphtha
solvent and apply it again.

I have not used a Brush-On Lacquer as suggested by Larry Toto but I
will surly try this in the future.

Between the final few layers of lacquer finish you should use a good
400-800 or even a 1200 grit sandpaper with water as a lubricant.  Wipe
the wood with a slightly wet cloth and sand about 6-10 strokes, wipe
the wood and sandpaper with the wet cloth and continue sanding.  Note:
you only want to use wet sanding after ALL parts of the wood are safely
sealed by the Lacquer.

Another trick is to use a very large, flat piece of thick plastic for a
sanding block.  The larger the sanding block surface is, the flatter
the final finish will be.

Good Luck from Phoenix AZ.