i buy backs, heads and feet for chicken broth. the meat you're leaving on the bones isn't adding much nutrition to the batch. if it's all cooked, take that off the bones and have it later in your soup.
i don't like celery in broth -- it makes it too bitter. i use onions, carrots, garlic and ginger. black peppercorns and dried thyme.
"simmering for several hours" in a crockpot isn't leaching enough good stuff out of the bones. i don't have a slow-cooker, so do mine on the stove and i cook it until the bones are soft. this usually means at a pretty hard simmer overnight -- even 12 hours.
i strain out all the solids and discard them. then i boil the broth to reduce it for easier storage. (i make LARGE batches, so i only have to do this a few times per year. like 15 pounds of bones at a time.) i do not skim the fat. animal fat is good for you and damn tasty. my broths are reduced to a very solid gelatin, that i need to break with a spoon for a serving of it.
As I ate the oysters with their strong taste of the sea and their faint metallic taste that the cold white wine washed away, leaving only the sea taste and the succulent texture, and as I drank their cold liquid from each shell and washed it down with the crisp taste of the wine, I lost the empty feeling and began to be happy and to make plans.
– Ernest Hemingway