Hot take, fat camps don't work because you're throwing a fat kid into an environment where he's forced to eat broccoli and fried unseasoned chicken and maybe some peanut butter sometimes.
Humans are creatures of habit. If Timmy likes chocolate bars, take away the king sized chocolate bar and give him one bite sized one every day, throw in an exercise program, and cook delicious main course meals.
Your success rate will fucking skyrocket.
If you operate strictly on a reward mindset you might start "rewarding" yourself with your cheat days when they should be scheduled, or at the very least spaced out.
Human brain is tricky.