I have a similar method of piling things in the run. I don't add bedding and poop to the run though, just grass clippings, leaves and other yard waste (weeds, garden trimmings, etc.). I have compost bins for the poop and bedding along as well as some of the other yard waste that I add there instead of the run. When you clean out the run to add compost to the garden or other plants do you pile it first for a few weeks or even months to cook off the excess nitrogen?