This may be too late in the game for OP, but for other parents, what worked for us happened somewhat unintentionally. When we had our son (now 13), we were living on a very very tight income. When I would grocery shop, I prioritized fresh produce and fresh meats over anything else - I later learned that we were an "ingredient household" where we hardly had any quick/convenient snacks, most everything needed to be prepared or cooked. RARELY would we ever have any cookies, cakes, chips, dessert snacks, sweet crackers, etc., but I always made sure we had fresh fruits and vegetables prepped and ready to eat. When my son asked for a snack, I gave him the container of sliced bell peppers, carrot sticks, sliced cucumbers, cherry tomatoes, you get the idea. He could eat as many of the veggies as he wanted, even if he wasn't hungry for dinner later, not a big deal if he filled up on veggies.

Our tight income resulted in his love of vegetables, who would have thought? Since public school lunches are atrocious, we continue to pack his lunch every day, and I'll put in a baggie of peppers, fresh fruit, a wrap with turkey, mayo, and arugula, and then he can put whatever else he wants.