I keep my beetles on rolled oats so the eggs can drop through the screened bottom without all the bedding sifting down. Mill run can be in the tray that the eggs are sifting into.
I use the mill run or wheat middlings only for worms that I will be feeding out to the chickens since it grows them half again as large as normal. However, mill run is so rich in protein that the larvae keep growing and by the time they pupate, which few do, they've run out of time and energy for the pupae to reach adulthood. Therefore, I cannot recommend mill run for beetle bedding or bedding where you expect to be keeping pupae that you wish to morph into beetles.
I use the mill run or wheat middlings only for worms that I will be feeding out to the chickens since it grows them half again as large as normal. However, mill run is so rich in protein that the larvae keep growing and by the time they pupate, which few do, they've run out of time and energy for the pupae to reach adulthood. Therefore, I cannot recommend mill run for beetle bedding or bedding where you expect to be keeping pupae that you wish to morph into beetles.