You could just put an ice pack in his lunch if you are worried about anything spoiling. He shouldn't eat tuna more than once a week b/c of all the mercury in it. Will they let him have sunflower seeds in his lunch? It is a GREAT source of protein too. Just FYI peanut butter has a lot of sugar in it too and I would try one of kinds that is sugar free. You can even try cashew butter and almond butter for variety.
I think it is great that you noticed about him being sensitive to all the sugar. He will do a lot better in school if he can think clearly b/c it can give him brain fog too. You know another reason that he will want more and more of the sugary foods is b/c they are addictive too!!
I also give my kids a fruit smoothie. I put a bag of frozen fruit and 2 eggs (I just clean the outside shell before putting them in b/c that is where all the bad stuff is.), add goatein protein powder (due to cow milk sensitivity), add honey if needed for taste depending on the fruit and 1 T of coconut oil. It tastes good and is good for you w/o sugar and and has protein! :-) I know you can't really send that w/him but he could have it in the morning w/breakfast or when he gets home for a snack.
Also, I just wanted to add that there are a lot of different types of cheese. He may like a different type. Due to the milk sensitivities/allergies in our family, we eat goat milk cheese or sheep milk cheese and it tastes WAY different from the traditional American cheeses. I can get them at HEB or Kroger. My HEB has a lot more selection tho. Of course, you can always try the health food store and you can find something new too!
Blessings,
M.
Mom to 5 Kids
www.4MyChildrenSake.com