I was going to post a similar question and ran across your thread.
We too have used grass clippings for about 2 months now (in the run, not the coop) and it does seem to work out very well. Like others have said I dump it in a pile or 2 and before you know it the hens (5 here) have turned the piles into a 2" shag carpet in the run. The grass absorbs the poop great and after about a week I'll rake it up and add it to the compost piles and replace with fresh clippings. Grass clippings are high in moisture so 2" deep is good enough for it to dry out quickly and not get clumpy/moldy. Since it is so moist and green I do not use it inside the coop but rather use dryer pine shavings for coop floor and nesting boxes. Good to know too about the shorter the clippings the better for digesting. Our "lawn" is just a mix of wild grasses and weeds with clover, no fert or other treatments involved, just rain. When I mow I try to concentrate on the clover areas to bag up mostly for the run. My 2 cents.