Earlier quoted context omitted.
I have an autistic kid who went through a phase where she would only eat McDonalds chicken nuggets... I live in a city and have 3 McDonald's pretty close to me, and the price for the same order of nuggets would vary by up to 50 cents between the 3... the cheapest place is only a half mile away from the most expensive one. It really is strange.
I don't mean to be rude but I'm just curious... did you try simply not giving them junk food? I have done some research on this and have not found any good evidence that most autistic children will actually starve themselves for any meaningful amount of time if their picky foods are not provided.
Our final diet for her was based on recommendations from her pediatrician, dietitian, and therapist.
While she might not have starved if we withheld chicken nuggets, she became extremely distressed and disregulated, which lead to other problems.
She has moved on from chicken nuggets, but her eating pattern is still the same. She will have only one food at a time that she will eat for proper meals, and that food will rotate every few months. After a few months of only eating one type of food, she will suddenly declare she does not like it anymore and move on to something else.
Her current food is actually Chicken Tikka Masala from one particular restaurant. Hopefully somewhat healthier than nuggets, although it gets expensive.