Fair point, however doesn't the park generally disclose ingredients or, in your case, cooking oil type, upon request? I can't see them willing to either expose a guest to allergens or forgo the revenue from those same guests skipping eating at the park without actually knowing if they are allergic to anything.
I was thinking, for this location - a vegetarian/vegan focus. Possibly a lot of snack items, going with a backstory related to either favorite meals of some of the explorers or something to do with dishes inspired by the temples found.