I'm not a mealworm expert, but I raised superworms for a while.
The big guys usually pack them in some kind of bran. (In your case, oat bran sounds fine, they can chew their own food.)
Just keep it dry so it doesn't mold, and keep a few veggie slices on top for water content.
Superworms, in my opinion are a little less demanding than mealies, my superworms lived fine on a diet of substrate from my box turtle, which was mostly peat moss.
When I was a kid and I ran low on superworms, (I lived on a farm.) I would just wait until midnight, and go in the grainary (Grain on the floor.) and sweep the floor into a dustpan. That would be a few thousand adult beetles. That would supercharge my colony.
During the day you's maybe see 1 or 2, but at night the floor was covered with 'em.
If they can live on cracked corn dust, they can certainly live on rolled oats.