Optimizing I from the start seemed like a too hard task, so I aimed for max throughput at period 4.

Machine operates at 15 products per 136 reagents.  Those are inconvenient numbers, so this is built around 45 products every 408 reagents, which allows it to be based around a 12 product loop.

The left inner pipeline takes 6 reagents and produces Silver-Gold-Silver, and a Copper, with some leftovers.  The right inner pipeline takes 4 inputs and produces Gold-quicksilver pairs.  These two work together, using 10 reagents to make a product at a rate of 1 product every 24 cycles.

The left inner pipeline is located where it is, because it's the only "donor" pipeline in the machine.  Putting it here lets it give iron to the right side, and Q-T to the final pipeline.

...Which is a monster, producing 11 products every 408 reagents.  Eight of these 11 have to produce two silver via purification, while the remaining 3 have to produce only 1 via purification.  The key here is the copper-quicksilver stick builder, which accumulates each until it has 7 or 8 copper and 10 or 9 quicksilver.  This results in 3 different unique sticks having either 7 copper and 10 quicksilver, or 8 copper and 9 quicksilver.  The stick gets passed to the machine in the bottom left, which is able to handle all three, and builds a product via a very slow, conditional pipeline.