Essentially, you have you henhouse, and attached to it is a small yard, for scratching. To that yard is attached 2 or 3 larger runs, filled with grass, that you rotate your birds to every few days. This provides them with grass, but doesn't allow them to scratch up all of your grass. Instead, when the runs are not being used, the grass, recovers. I'd probably use a 3 or 4 day, or a one week rotation. That way the grass has a week or 2 to recover.
I've penned out a concept where the house would have 2 pens, of 8x8. Each pen would have an outside scratch yard of 8x8. Each pen would bea attached to 2 runs, roughly triangle in shape, that would be 32 feet on the straight sides and about 45 on the diagonal (think of a 40 foot square divided in 2 diagonally). I'd plant several (3-5 per run) semi-dwarf fruit trees in the runs to provide shade and windfall fruit for the birds, and regular fruit for me. I'd reseed portions of the run each year with clover and small grains as well. The run would have a 6 foot high fence. the yard would be about the same, but covered with netting.