I made containers for it by tying four pallets together. This helps to keep it in one place. I have a total of five containers in total, all in a row so, after the first one, I only needed three pallets to add to it. I always plan to cover it but never actually do.
When the goats are cleaned out and the contents of the shed put into the heap, it gets trodden down. My grandchildren used to love that bit. Wellies and old clothes on and they used to jump up and down on it.
What I can't use on the veggie beds, I offer on freecycle and people just come a dig out what they want.
How often are you cleaning your goat shed? Mine gets done after a couple of weeks or so, but I do keep adding bedding to the top. In the winter it gets left for a couple of months as this helps to conserve heat for them. Providing the top layer is clean, they won't get mucky.