You just solved your own problem with the sod!
Since you're digging up your yard anyway, just cut sod from your lawn and use it for a salad bar. This way there is no need to buy harmful fungus-sod.
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That is what I figured about the sod.
Right now we don't even have dandelines to pull...
Make a salad bar. Make a square or rectangle out of landscape ties and cover it with hardware cloth. Seed underneath this or lay a strip of sod beneath it. The chickens will be able to peck pieces as they grow but won't destroy the roots.