Do NOT use Keyboard Carriage of Indiana. They were the house freight unit of Kimble factory, and are equipped to move freight for factories and warehouses, mostly. they showed up at an organ move for an organforum.com member with only a carpet dolly and two clueless drivers.
Most of the big moving associations had franchises that had equipment for moving grand pianos. This takes at a minimum, a piano board from New Haven Moving Equipment Co, a 4 wheel rubber pad dolly with a 1200 lb rating, and some flat (not round) nylon straps and pads. Ensure that if there are any stairs, or even one more than 3" high, that there are four strong men, of which one must know what he is doing. (ask about the music rack and leg removal as a test before they start work). Your technician should remove the pedals before the four men show up.
I worked 1973-4 at a North American Van Lines agent that had this equipment and the one driver that knew what he was doing. The industry has since contracted and now the majority of moving vans I see on the freeway now are Allied Van Lines and Mayflower Van Lines. North American since their purchase seems to have moved into the Electronics and trade show market, mostly.
Be sure your music rack is securely strapped down, or removed and inventoried separately. Make sure your bench and legs are inventoried separately. Buy the insurance.
My console piano was moved competently from Herington KS to Louisville in 1983 by an Allied driver with a helper. It did not require a piano board, being a console. They carried it down the stairs.