Stocks don't get good until they've sat out for a couple days!
Seriously though, if I start one too late in the night to put up, I just bring it to a boil, cover it, and turn off the flame. It cools down to the next morning when I can deal with it then. If not, bring it to a boil again, and put it up the next night. This is the point where I strain out all the solids. No reason for the bones & meat chunks to stay in the stock after the initial simmer.
The fat skim gives a protective layer once it solidifies.