I think there was a time when a few teams allowed RV parking - folks would come in for a series and stay at the stadium. IIRC, Kansas City might have been one of them, but I wouldn't be surprised if the policy had changed. Teams are probably leery of having folks on the premises that they might be held "responsible" for.
I did take in a series when my favorite team played the Tampa Bay Rays, combining baseball & the beach by staying at Fort DeSoto. However, I'm in a Class B; might be trickier for larger units, but isn't that what you have a toad for?