To start the rate calculations, I turned this into a math puzzle: Given the input [1, 2, 3, and X], create the output [5, 5, 5, 6, 6, 6, X, X], with the highest ratio of output to input. Within a day, I had this solution, 11 inputs to 1 output, but I kept searching. I realized that in a perfect solution, gold must only be made with silver + quicksilver, and the remaining quicksilver should only be used to make silver from copper. 

As I was narrowing in on a 20ish-rate solution, I decided to "quickly" put my old 22 design into the game. That was when I realized I’d underestimated the implementation phase. My self-imposed challenge of no pistons and no pivots got in my way, and I could feel my sanity depleting. While I loved the logic optimization part of it, maybe building these machines isn’t for me. 

In the end, I'm happy my process led to a solution, but I wish it was less of a monstrosity, and that I had the energy to implement something better.

Enjoy?