Here are some ideas:
#1
How old are the kids? How about doing a watermelon carving contest using the mini melons? The one I'm thinking of is a Thai technique that is exquisite. The carvings look like flowers such as peonies etc.
Here is a step by step guide on doing it:
Watermelon Carving in 18 Steps | Fruit Carving | Temple of Thai
And here are some examples:
‰Z‚Q‚O‚O‚R Watermelon bowl
I've seen whole bouquets done of various melons (watermelon, canteloupe, honeydews along with other fruits and veggies and it is absolutely breathtaking! Wish I knew how to do this!
#2
You could all make a "signature dish" that is distinctly describing you, then vote on who's is the best.
#3
You could all make the same dish and see who wins....like you could do a classic souffle (not very 4th of July-ish) or maybe your could do a patriotic baked alaskan or something like that and see who wins?