My neighbor went through that, when she started couponing heavily after their cupboards being bare for a long time because hubby was out of work, 5 people in the household (three teens) and she on disability for MS.
So, it took about three months before they devoured everything in sight - then it became "we don't have anything to eat" even though the cupboards were jam full
So it sounds like your family is enjoying the huge amount of food options now that you're able to get more.
I'd find a way to hide as much as possible and leave out only that which you don't mind them opening and getting into - then slowly add to it as it dwindles.
Even if it takes 'hiding' under the bed in flat storage bins without them knowing about it 