We visited for 8 days last year and managed to stay gluten-free (plus, I don't let my kids eat a lot of sugar). We brought in a lot of foods/snacks that kept us going - maybe some of these suggestions will be useful to you?...
carrots
dried fruits
raw almonds
no sugar-added applesauce cups
sunflower seeds
raw fruit (bananas, oranges, apples, etc.)
we also brought in banana chips, but they are made with honey so you might not be interested in those. Seriously, I could make it through an entire vacation packing in only these types of foods and grabbing a salad here and there. Especially when it's hot...I don't feel like eating at DLR when it's hot, anyway. My kids can have dairy, so we also packed in yogurts and cheese, but it looks like you're avoiding those.
We bought the skewers at Bengal BBQ on our trip previous to that one and thought they were terrible.
The sight of those greasy turkey legs makes me sick, so I've never tried them, but a lot of people on the boards seem to think they taste really good.
Hope you have a great time!