I like the cabbage idea.I use rolled oats from the feed store and cabbage leaves for my moisture. I had problems with carrots going moldy. The cabbage leaves will dry up completely before they think of molding, so it has really been working for me. I like that the oats stay in the sifter for the most part...that way the frass can be removed. I find it less stinky if I can do that once monthly. I do see the benefits of the bran though. But, my chickens like getting some oats with their worms, so it works out.
I wonder if the mold is coming in on the oats?
When I tried using grain from the feed mill for growing fodder, I had much more molding problems that when I used health food store grains.
Then again...wonders since they are rolled oats, they might be exposed to heat during the rolling process.
Just pondering possibilities.