I don't know about the car wash application, but there is a foam-like filling that I've seen used in construction equipment tires that keeps them from going flat. I does make them into a "solid" tire and prevents them from going flat. It is available at a local tire store, so you should be able to find it readily. It does add a lot of weight to the tires on a bobcat. I don't know if weight would be a factor on the car wash machines.
JPRB