I work with a mover who has done quite a few long distance trips.
With heavy upright pianos he likes to place a length of board, front
to back under each end of the piano, just thick enough so that the
wheels will be off the floor.  This to avoid breaking the metal
casters, which sometimes happens as the piano gets jolted around
a bit.  (I assume the quality of the vehicle suspension, and of the
roads traveled, can be a big factor.)

In either case, the piano is still wrapped in moving blankets and
strapped securely to the side of the moving van.  There are occasional
uprights which because of their construction do not sit well on boards,
nor dollies for that matter, and have to rest on the casters.

Professional movers will generally bring the piano from house to truck
on a dolly,

Richard Friedman
Upstate New York