I've been using hay exclusively and have not had matting problems at all.
Just fluff it a bit before laying it down. Hay off the round bales will come off as sheets sometimes. Those will certainly mat. But my chickens just worked at it a little more and did fine with it.
Works for me...
I should have mentioned the very large run is hay-covered, because it is next year's garden, ala "Ruth Stout".
We get torrential rains (just had some), and the hay seems to handle it.
We also have very fertile soil, so it breaks down quickly. As a gardener, soil health comes to mind as the...
OTOH, I use only hay. It's because I can get it at a good price compared to other things.
I turn it once a week, esp. under the roosts. I've never had a mold problem or problems with it breaking down, although I will say that coarse hay works better than fine hay.
My birds don't really...
This winter I had only 3 chooks in mine, and I use deep litter.
It would seem that chickens can poop while they are asleep! Just look under the roost in the morning and notice the "line of poop" that forms directly under where a group of birds was roosting. What a great idea! If humans...
In my case, this year's run is last year's garden. My chooks will turn the hay all day long every clement day of the year.
Let them do that and they will accelerate the softening of the soil.
Sure! Since it isn't stinky, and there's no big disease ravaging your flock, then stirring is an option. But if you can't stir *any* dirt with the litter, then stirring is a waste of time. In that case, only nature and time will soften the earth up enough to stir.
But if you're able to mix...
If you could till/plow all of it together that would help things out a lot faster. But if time is not a factor, then do what you're doing and then just let nature take care of it.