What kind of feeder do you use?
I like my traditional, hanging feeder, which I have in a shelter so that it stays dry.
I live in the Steamy Southeast of the USA, where 95F with 95% humidity is our summer normal, and have never had feed rot/mold unless water was directly getting into it.
Since the life of a mouse in a chicken run in the daytime is short, your better option would be to either switch to a rodent-proof feeder or to put your feed into a secure place (in your house, inside a metal garbage can, etc.), at night.
I personally limit scratch, empty carbs, to a few handfuls a week -- thrown into the run in whatever place I think needs to have the litter turned over.
I don't limit green stuff like weeds, veggie trimmings, etc. on the theory that they'd be eating plenty of greens if they were free-ranging.
I don't find that my birds over-eat fruit. I give them melon guts and rinds, bruised apples, and various peels and they generally eat some and leave the rest to become one with the litter.
HOWEVER, I'm sure that if they didn't have free access to their feed at all times during the day they would gobble down anything that appeared without self-limiting because they were HUNGRY. Chickens are designed to forage all day rather than eat bulk meals.
Scratch is empty carbs. The pellets are scientifically designed with the perfect balance of nutrients to keep chickens in optimal health.