I'd suggest seeding clover. But I like clover more than grass. The white clover stays short while the red and crimson get a foot tall.I'm having a big, dead tree taken down so there will be woodchips, but mainly I use pine straw in the run because it's free for the raking on my property.
I'm looking forward to seeing what the ground is like under the current run when we move the chickens to the new Chicken Palace once it's finished. I have to put it back to grass and I expect to see really AMAZING grass there next summer.
Yep, the grass and weeds will attack the fertile soil with a vengeance. Plant a garden! The tomatoes really like the soil.