Chickens live off corn and grain because it is a cheap thing to feed them not because it is ideal nutrition, and the idea of corn "warming" birds seems more like a often repeated wives tail than anything else. Do you have any actually scientific information about this? If so I would love to read it but I have never been able to find any. They certainly do not NEED corn.
I have definitely seen farmers at farmers markets selling "grain-free" eggs. They do this by feeding a pastured or fodder-based diet so they are being feed grains as grasses rather than as processed grains if that makes sense. The nutrition difference is huge and with fodder you can turn 1 lb of grains into 6 + lbs of greens/grasses.
I think that if you did enough research into nutritional needs/balance and worked it all out so they are getting the right protein, calcium and amno acids I think it could be an amazing diet. Likely much better than a standard commercial diet -- I am not sure what your costs would be. That could be an issue.
I feed a corn-free, soy-free organic feed and then grow my own organic wheat/barley/BOSS fodder and noticed a big different in feather quality and egg yolk quality versus commercial soy based feed.
I would love to know what you need up going with!
https://www.backyardchickens.com/t/713334/growing-fodder-for-chickens
That's just what I've been taught by the people that got me started in chickens, I don't have any scientific evidence.