This solve is the brainchild of a remarkably iterative process.  Or perhaps not so remarkable, given how often that happens in production C...

Anyway, we targeted input-speed 14R from the very beginning.  Our first strategy did this conventionally, with two pistons pushing inputs at P4. The problem was that all the supporting machinery limited us to only 2 purifiers in the left chamber and 3 overall.  That stressed conduit use and overall geometry significantly.  Our opening bid clocked in at 209c, with gradual improvements dropping to 166.  But we were stuck at 24R, with the input pistons sitting idly for significant periods.

Looking at that constricted rate, we reasoned we might as well try pseudoperiod 3, which minimizes to 21R and can use much less machinery.  The pair of pistons was replaced by a full-tape hexarm, and we could now fit 4 purifiers and run at a much more relaxed cadence.  The hexarm did need to pause for one cycle to extract the atomic lead needed for the product, but we achieved 22R on the first try.  New benchmark set at 152c.

Looking to cut that last rate point, we turned for ideas to Dental Amalgam, a recent cabinet puzzle that also utilizes pseudoperiod 3.  Here we must credit ebonnov and Transcendental Guy, who demonstrated the power of the 
 fully-loaded triangle track handling inputs.  This takes the same footprint as the hexarm, but the independence of the grippers freed us from the need to pause.  It also trimmed some latency: new benchmark set at 21R, 140c.

After puttering about with Sum for a while, we returned to Cycles.  And it was immediately, blindingly obvious that the tringle-track input strategy is by no means limited to pseudoperiod 3.  It can theoretically move at input speed--that thing we tried and abandoned at the start!  In this geometry, there is a 1-cycle pause each time the lead purifier triggers, but very little adjustment was needed for the very same machine to reach 14+3=17R.  All we needed to do was add a third arm to the lower tringle-track, tasked with extracting one copper form the usual flow.  Massive drop from 140c to 117c, and here we rest.

We see no reason, on paper, that 14R should be impossible.  In addition, we use a purification strategy that creates iron last, which is the very worst possible for latency.  Based on that, it seems like sub-100c is very much on the table.  Whatchu got, Morraconda?

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NB: We felt bad for the hole in the center of the output, which was the only hex without its own glyph or mechanism.  They looked sad.  So we decided to award them a shiny calcification glyph.  100% unique!  Nobody else has one!  You deserve it, donut-hex.