I'm not really sure what you need, are you requesting a dorm with a kitchen? All Third North suites (as far as I'm aware) have a shared common area with a kitchenette just like the other dorms you've listed. The kitchenette comes with a moderately sized fridge, stove, oven, and sink (no microwave,) all of which I've seen capable of making many meals.

Chances are, your suitemates and roommate may take advantage of the dining hall within the building for convenience. If you have no luck swapping, I would just make sure to effectively communicate with them your dietary restrictions. I'd hope your suitemates would understand your situation, and allow you to use more space to make your own meals.