sound reduction/grand piano

You are headed in the right direction. I would also suggest sitting the 3 legs(casters) on rubber sound isolation blocks, of the same type that commercial HVAC units rest on.This will significantly reduce the transmission of sound/vibration into the floor,which your neighbors downstairs should appreciate.

You probably don't want to go the route of hiring a company such as Acoustilogs to investigate how noise travels in your particular apartment building since they are quite expensive. If the piano is anywhere near a vent through which noise travels in your building such as a bathroom vent, you may want to shut the door to that room before playing the piano. As a courtesy, don't play the piano before 10:00 a.m. or after 8:00 p.m. which would be very considerate since some people don't sleep traditional hours. We had a neighbor who used to play the piano at 7:00 a.m. before she left for work and the piano was right near a wall which adjoined our bedroom.

I have my apartment sized baby grand (only about 5' in depth) , with its 3 legs sitting on an octagonal area rug.

Further insulation is provided by my larger dog's bed, directly under the curve of the piano, & my smaller dog's bed, which fits perfectly under the bench (only the pedal assembly separates their little bedroom suite).

Never got any complaints - but, truthfully - I dust it more than I play it.

If anything, it functions as a most beautiful indoor dog house!