Not all have been turned into Franken-chickens, luckily. OP might want to look into some of the less productive breeds. The Russian Orloff springs to mind...I'm sure there are plenty more. But the less they've been bred to rapidly turn feed into meat or eggs, the more I'd think you'd be able to get away with not feeding them commercial feed.
Very true...I think most would agree that heritage breeds would be better suited for this than production breeds. I'd think a smaller heritage breed would be ideal as it'd require less calories overall compared to a very large breed.