Oh, I also have a rototiller... I imagine I can just till the run to turn it all over.
I have a small 10 inch tiller attachment that attaches to a 40v weed eater power head. It is perfect for things like turning over compost in the run. I used that method myself when I first started composting in the chicken run and the litter was only 4-6 inches deep. When my chicken run compost got to be 18 inches deep, the mini tiller only fluffs up the top 4 inches.
But yes, my mini tiller is faster, does a better job in tilling, and saves my back. Just make sure the chickens are not around the tiller when in use. Even using a pitchfork requires care not to accidently stab a chicken running underneath you. I prefer to do any tilling, or turning, before I let the chickens out of their coop in the morning.
If your compost is too deep, then you might get clumps of compost stuck between the tiller tines and the splash plate above the tines. That happened to me a lot and cleaning out the jam was a pain in the butt. I ended up taking off the guard and now it works much better and does not clog up all the time. I think that it is safe for digging in compost to remove the guard, but I would not recommend removing the guard if tilling in soil where there a much greater chance of throwing stones back up towards your face.
A standard garden fork used for digging would work in compost, but a better option is a 4 or 5 tine hay fork. I bought a long handle 5 tine hay fork and it is much better for working in compost than my garden fork. Dear Wife does not understand why I have a short handle 4 tine garden fork, a long handle 5 tine hay fork, and a 10 tine manure fork. I use them all, but for different jobs.
At 18 inches deep, my chicken run compost is now too deep to turn it over either manually or with a tiller. But I don't worry about it because I layer nitrogen and carbon sources as I built up the litter. It never smells.