So there are no dirtier or cleaner parts, it's equally bad all over?
You might be able to just rake off the topmost bit regularly, not too big a job if you toss it straight out the door into the run, and then put down a bit more bedding if the total is getting too thin.
If you don't want the chickens in the rafters, I would try to block them off somehow, maybe like
@Ridgerunner suggested:
Of course the chickens WANT to sleep as high as possible, but if you block them out of the rafters, they will get used to the new situation pretty quickly. I assume you have roosts where you do want them to sleep.