I would doubt to try for a tailgate at all. Last year, I had to park far up the road, and walk the distance to the park. (And there were players and their families who had to walk much farther than me.) (Also, last year, the game was played in a constant downpour. But the weather reports look for it to be perfect this Saturday.)
Remember, this is not simply playing a game in a park; it is playing a game in the middle of a tournament taking up six sites and 22 fields at Independence alone.
In such an environment, I doubt that they would allow open grilling. My best suggestion would be to grab your six-packer, and fill it with a couple cold-cut sandwiches and your favorite (non-alcoholic) beverage.
You can always look up details at
http://www.cantoncup.net/