Thanks AT, that is a pretty cool breakdown on what is at play.
I know that different elements precipitate out when the planetesimals form and that comets stir up the mix by adding volatiles. That is why we have so much iron and uranium here. The both precipitate at the same temperature when the planetesimals formed that made up Earth.
I guess I have a significant unknown, in the sci fi future what kind of elements will be used for making things. For example there might be heaps of carbon used instead of the steel of today. In which case the answer can not be found.
Strictly IMO speculation, but I think that the modern electronics industry offers a good glimpse into the future ...
Most electronics start with silicon, which is just stupid common (like Carbon or Hydrogen or Iron or Aluminum), so what really drives technology are the small amounts of hard to get stuff (like gallium) that make all the difference in the world. So even if the future of civilization is marked by a massive shift from Structural Iron to Structural Carbon, most of the cost for a high tech carbon widget will come from the trace elements needed to alter its properties for the application.
So I suggest focusing on all of the rarest elements and just assume that someone will need it for something.
A gas giant may have access to surplus Xenon gas, Mars may have access to surplus water soluble Boron, the asteroid belt may have access to surplus 'Platinum group' elements (dense metals).