Our 25x50' run which housed 25 CX and 25 FR's last summer season (two batches) is definately worse for wear. The places the tractor sat more than 2 days are devoid of all vegetation. It's simply mud. Due to drought, I was unable to water the poo in (and the skies did not provide either). I did rake it out best as possible, overseed in the fall and I'm still waiting to see if the grass is going to come up in places.
Because you do not own the land, I would be exceptionally cautious proceeding. Yes, when the chicks are small, the damage is minimal. However, as they grow (and produce more), that's when the damage is done.
I did feed fermented feed. It does help tremendously with consistency of poo. Instead of watery, it's solid enough to scoop up on a shovel. I would do that as well as much as possible. Raking it in just makes the mess continue further - especially if the land is on a slope.