I just expanded my flock and hear you. My oldest, most productive hen loves chicken feed. She used to live with my chickens (this was a BAD idea - a brood hen killed 2 other birds and would have killed this one without $200 worth of vet care). Despite her past injuries, I have to lock her out of my chicken coop when my hens are wandering or she goes in to gorge herself.
The good news is that she is charming, having become so enamoured of chicken feed that she flies over whenever I am in the backyard and begs for it, eating out of my hand. She has taught the entire flock to do eat from my hand by example. In fact, a blue jay is thinking about joining them.
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I feed crumble, not pellets, because it takes longer for the chickens to eat it and this keeps them from picking at each other. It's also a better size for the pigeons. I feed very good, but expensive seed to the pigeons. I've taken to putting my feeder on the lid of a storage bin. When the seed gets scattered, it's on the bin, so the pigeons can still get at it. I scoop it up and pour it back into the feeder. It's not just 'preferred seed' (although I have yet to find a bird who really likes buckwheat). They also just get into a lot of seed and toss it because they seem to like to better off the floor than from the feeder.