No, this exists between DC and Orlando on Amtrack. I considered contacting Amtrack to charter a car train to my location to another. They'll probably do it for enough money and it's not that much money.

What you need to know to argue is, say, they're not losing all of the berths on a vehicle transport car if you want to move one car. They're having you pay the upkeep for that one trip which is not the same as the fully loaded vehicle car.