If it were me, I'd pay it safe and "double" check! What I mean by double is both email and phone. I would think that if you could reserve an area, they would have a diagramed map online where you could see which areas are reserved and which are vacant, and book right on the site. Good luck and have fun!
It was years ago...but we had a party using the wooden tables by the parking area under the trees...but I would check Elizabeth is right!
Check with the office to see what they have for groups.
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