The antique car restoration community deals with this problem
frequently.  You can use a high quality body filler which can be
easily sanded down to a smooth surface and painted as you like.

I've filled, smoothed out and painted many castings for differentials,
transmissions, etc., in this manner for prize winning antique car
restorations.  I don't know any reason why it wouldn't work on a piano
plate.  Body fillers are available at any auto paint supplier.

Joe Teagarden