Another thing I have pulled when going into these places that dont allow you to bring food in, tell them you are diabetic and you HAVE to carry food (protein bars for example) on you at all times, incase your blood sugar dips.
Ive done this in movie theaters etc and the staff wont question it if they think its for medical purposes.
UPDATE--
Wasn't too hard to eat decent! There was more of a selection at the park than what it showed online. We walked so much I burned off anything I ate, no desserts/sugars consumed though. My weight stayed the same but I'm sure my metabolism was kicked up though! Walking fast all day for conference and the parks was great.
Make sandwishes and meals in tubawear and leave it in your car, lunch go to your car and eat, anything else bring some protein bars inside your pocket, bushgardens should have those giant turkey legs, eat a couple they are delicious!