Can't say about the lamb fat; I've never had enough of it to make me want to take the effort to save it.
As far as the stock cubes go, I've done this for years. Very handy to be able to pull out just a few cubes to mix up some stock when I need it.
Are you straining the broth after cooking it? I'm not sure I understand why you still have solids to puree. And the ham stock sounds perfect; lots of gelatine to make it set