areas in the lot with no ground cover or grass at all due to the dog
running around. This leads to a lot of mud on the dog, and prevents us
from putting him in the car as often as we'd like to go to the park,
etc.

I would suggest getting a cage for the car so that you can put him into it and
not muddy the car near as much. Also, you could give him a cement dog run
outside. Then, he'll only get muddy at the park.