Need advice: first grader won't control cafeteria spending

Final edit: thanks for all the feedback! We have found a portal to the school nutrition service. No live person, sadly. American South school lunch is a joke, no doubt. He's a great kid enjoying free (in his mind) junk food, so I know the answer has to come from the school itself.

Original post: My 7 year old son seems to think the school cafeteria is his personal smorgasbord. He will buy 2 breakfasts, lunch, fruit snacks, ice cream, cookies, etc.

The deal has always been he and his 3rd grade sister buy school lunch ($3.25) daily and once a week can buy an extra treat. Sister has no issue and has been doing this since kindergarten.

They eat a huge breakfast at home, and we have him take an extra snack for mid-morning so he can eat before lunch. Not helping.

Nothing we have tried is helping our son control his impulse spending. Here's what we have tried:

1. Packing his lunch. He still buys snacks and breakfast.

2. Taking his money to repay. He was upset, but kept spending.

3. Grounded him from Minecraft/screens for every day he spent extra. Nope. Devastated but still spending.

Endless discussions, talking about stealing, impulse control, etc. He isn't starving, we have plenty of food at home. He's buying junk - cookies, ice cream, etc.

The school understandably will not turn down a child buying food, even if their account is in the negative. They'll restrict some purchases, but still let him buy breakfast, for example.

This child can easily spend $40 in a week. We have the money, but the principle of the matter is making us crazy.

Help!

Edit: this school does all the purchasing on a charge basis, there is no cash exchanging hands. The kids enter their ID number and it charges an account that I control. I put in $15 a week for each kid, which is enough for daily lunch and 1 extra.

Edit 2: he will freely admit that the food is for him. He says he just can't resist the junk food.