Perhaps consider building a second run maintained with deep litter. Let that be their primary place to be. The wood chips and other material help their droppings stay off the surface and breakdown. For that to happen out in the open, you need a pretty large area. Then, you can let them out...
Is their run of sufficient size to not let them out? If you want to protect the grass, you very well may need to keep them off of it for some months.
Pictures would help people to give advice.