I mostly use wheat bran, oat bran, and when I have it I mix in some non medicated chick starter. I find thinly slicing the veggies (Especially apples and carrots 1/8”-1/4”) helps keep the mold down, their favorite though is broccoli stems 1/4-1/2” thick, I’ve never had these go moldy.
I don’t think the beetles have “escaped”, but I have had some meal worm spills, thanks to chickens, kids, and cats. I just sift the bigger worms using two dollar store sifters, one with a fine mesh and one with a more open one.
I just leave the beetles in their drawer until they basically die off to 50% then move the survivors into the new pupae/beetle drawer and wait for the baby worms to grow. It’s not a fast process but quite low maintenance.