Last year I inquired about the counter service and carts through those phone numbers and someone emailed me documents listing some common items and the allergy information. It was detailed enough to list every food at every CS place but had things on it like where to find sugar free or peanut free items (wheat and milk free too - etc) and what those things were and it listed the ingredients of things like Dole Whips, pretzels, and what kind of oil the popcorn was popped in and so forth. My son doesn't avoid wheat but perhaps that sort of list would be helpful to ask for.
I have read that one can ask for a manger of the CS place and they should be able to provide you with ingredient information. I haven't had a chance to try it out for myself yet (last summer's trip got cancelled) but hope to get a chance this spring or summer.