I make my own food.
White Millet is very high in fat, red millet is a much better choice. All nuts are very high in fat, as well as sunflower seeds(which aren't good on a daily basis anyway), and spray millet is also high in fat. Apparently oats are also high in fat. Wheat seeds also apparently aren't very good for them either.
My home-made mixture goes something like this:
Bird seed mix(rape seed, canary grass seed, flax seed, white millet and red millet)
That's the staple diet. I feed just one, and it's about 1/2 teaspoon a day. You might also want to try feeding around the same time every day. Maybe your mice are gorging because they don't know when to expect food?
With the mixture, I feed so little for one mouse that he isn't exposed to very many of the high in fat foods like the white millet seeds and the oats, and if he is, it isn't every day. Like today I saw there were more red millet than there was white.
There's one dog kibble included in each feeding - it's a "minichunk" so it's not too large for him. And because I feed him just the right amount, he doesn't selectively feed and eats everything. He doesn't have food down in his bowl 24/7 either, he generally eats it all within one or two sittings.