If I've calculated correctly (and man, I hope I've calculated correctly!!) - the ratio is 136:15. I must be insane for wanting to give this a go.

Some details of my solve (feel free to skip):

Silver pipeline:
All 136 lead get purified --> 17 copper
All 136 tin get purified --> 34 copper
45/51 copper get projected --> 45 silver
6/51 copper get pulled (by the higher track loop) into the gold pipeline

Gold pipeline:
All 136 iron get purified --> 68 copper
58/68 copper get purified --> 29 silver
10/68 copper get pulled (by the lower track loop) and projected --> 10 silver
39 + 6 silver get projected --> 45 gold

The cadence of gold, silver, and quicksilver was so irregular, I found assembly difficult at anything less than 15P. But with an instruction secondary, I knew I needed a shorter period. The only solution I found was to brick enough atoms for all 15 outputs, then deliver those atoms at a regular rhythm.

I was able to get everything working at period 4, except for assembly, which I eventually got working at period 8.

Enjoy!