The aniline dye is the better direction to go.  The Behlin dyes from
Woodworkers Supply I have used many years with great success.  Very
small amounts of dye will produce large amount.  32 ounces will give
you an amount needed for the piano assuming it is 6 feet or under.  If
you let me know the color I can give you the dye amount to use.

The finish should be sprayed if you hope to achieve a closed grain
rubbed affect.  Deft is okay but on the level of a hobbyist.  I use
a lacquer from Randolph products in Calstat NJ.  I have used their
products since early 1980's and had excellence results.

I paste fill before the coating is applied.  Webb Philips produces
sells a filler I have found to be the best quality to use.  The
procedure I use is repair, sand 220, stain, wash coat, paste fill, wash
coat, dust sand, gross coating sanding sealer 4 coats, cross grain sand
to level (no voids), 3 medium precatulized clearcoats, wet sand 600,
000 steel wool and 3M hand compound for final sheen.

This note will most likely produce some other input from readers.
Their are many products and procedures that are used and other input
will be interesting.  Hope this will help your project Good Luck

Thanks  Don Dusenbury