Caitlin, that park looks like it might be kind of hard to get into...i don't know if you need to live in the area or not, but it says you need "a valid dog license from the county of residence"....
also, up here we have a couple of places, indoor and outdoor, where you can basically rent for a few hours for a "doggy party". They've got agility equipment and some other stuff for the dogs to play with. If you have many places like that down there, i don't know how much it would cost to rent a place like that, but if a bunch of us go and split it i don't think it would be too bad.