Actually,

In case of a piano move there are some companies that specialize only in piano moves, and those companies often offer flat prices for different types of pianos (in case your move is local) regardless of the time it requires to move it.

As far as regular movers concerned, 3 hour minimum is a standard requirement in the industry, most movers consider moves like that too small of a job, and I wouldn't go for any man-with-a-van for a piano move - after all you need professionals who carry special equipment and know what they are doing (needless to say they also need to be licensed).