I got overambition this puzzle, and started with a min rate attempt. I spent the first day making my left chamber. Because 7 inputs = 1 output, I needed the extra lead and copper to be pullable from both states (whether or not there's a metal already on the projection). 

After I got it working, I realized how much I'd underestimated the building aspect. I needed to project an iron, a gold, and build everything in 14 cycles. I eventually gave up and went for a longer period, but I kept my left chamber the same, as a memento. I'm sure I can lower the cost, but I'm not thrilled with the cycles anyway, so its good enough as is.

I might get beat by solves who purify everything in one chamber, but I honestly believe this approach is theoretically sound. If I were better at production maybe I could achieve my p28 2p dreams. I'm happy enough with this, and I'm excited to see the top solves :)