Forgive me if this has already been suggested: we had a friend with a packed-dirt run and she cleaned it daily with a doggie pooper-scooper, you know the type like a dustpan on a long handle so you don't have to bend over? They just scooped and composted. Worked well for them as far as I saw...
We have straw/hay but our run is covered so it stays dry. In fact oday is the FIRST time I have ever noticed any smell out there. We had a wicked, torrential, very unusal thunderstorm last night with sideways rain and the edges of the run got soaked. Hoping it dries out before too long, as I have very close neighbors....