Right now I have a 30 gallon plastic trash can that I store my chicken feed in. However, the lid is not tight enough to keep out the roaches from getting inside. Whenever you remove the lid to scoop out feed, roaches scurry all over the place. My Wife will no longer feed the chickens because of all the roaches that jump on her hands and arms.
Can you put the feed storage inside the chicken run? Then when the roaches come out, the chickens can have a snack.
Probably not a good long-term solution, but might be something you can do at once, while you're still researching other options
