I wouldn't bother trying to get the grass to re-grow again. Chicken manure is to hot and chickens will just scratch the roots of the grass plants until you have nothing again. The only way to keep your grass is to keep the chickens off of the grass most of the time. This is why the chicken tractor was invented.
So getting the run covered, and or getting a base down in the run is the way to go here. I picked sand for the base in my coop. I can pick up a bag or 6 of play sand and carry it in my car home. I then will add it as needed to keep the puddle covered up. (I had the first load delivered from a concrete mixing company.) Others have used large gravel. I can't speak from experience but that seemed like the gravel was going to be to difficult to maintain on the long term. Anything that is used will sooner than later have to be maintained. (Think digging up and out.)
The worst thing we tried was wood shavings and straw. Both items break down quickly in the rain and start composting quickly. That layer of material stinks very badly.
I keep wondering what concrete would be like. My thought is a concrete pad with a catch basin at one end. That way I could walk in with a hose, and hose it down. It would be clean again without a lot of effort. I do know that is my most favorite part of a new patio that was poured this past summer. I must say that not only do I dislike padding around in the mud, but I don't care much for putting down scraps of food for the girls directly into the dirty sand/mud/waste. I have a couple of litter pans that are easy enough to wash out, but still
I don't know what changed I used to do it like that years ago, and my sister still does.
I just got to thinking about my sisters set up, and realized that she and her DH put most if not all of their yard and kitchen waste into the run. They use their run as their compost bin. The girls keep it turned and tilled enough that about once a year they pull it out and dress the gardens around their home with it. They have rather nice flower and vegetable gardens to say the least.
I would also post this on the Oregon and Washington Threads. Index - Where am I? Where are you! - Oregon or Washington. These threads are going to be your best resource for our climate. Without living west of the Cascades, it is very hard to understand the climate. Both of the state threads are very active, and this is a topic that comes up fairly often.