Ahhh, yes. I recall the days (and there were only a few) of grass in the run.
I used a garden rake. Its good for break up the poo clods smashed down and stuck to the grass. It will take some exercise, so get ready for a work out.
Once the grass was gone I changed how I clean the run. I still go in occasionally with a rake, except now I use the leaf rake. Most of the time I go in with a shovel and rotate the soil so the poo ends up on the bottom and worms and bugs end up on top for the girls to have fun hunting. I only do a small portion at a time. The girls love it when I shovel! It also helps keep the soil loose to make dust bathing easier.
Seeing you're still at the grass stage, you're likely at the point of flies setting in. If you haven't heard about it yet, use DE (diatomatous earth), and use it liberally (learned that the hard way). You'll be amazed at how the flies disappear. When the chicks dust themselves it will help keep parasites in check on them also. I usually don't need to reapply the DE for about a month. The flies are my cue. It will also help dry up mud quicker. Another added bonus to DE is it will keep odor under control also.
Have fun and best of luck!