Here's a thought:  figure out what you think would be a reasonable area that they would need to park cars on..... tear that area up and plant a permanent grass on.  Then rip and rest and plant to your regular crops.  Next year, when it comes time for the "parking lot event", they may get the message to plant on the grass, and stay off the cropping area.  Yeah, you would still need to pay the rent on it.  However, this method might help minimize the area they run on.  It would be worth a try.