5 days ago I started to try to solve this puzzle for the first time.  I began with cycles before touching instructions.  My goal was period 6 machinery, leading to 18r on the large output.  I figured out a way to get metal and quicksilver through the conduit at 6r, such that there was a lot of flexibility on the timing relative to vitae.  It used a piston loop and filled the whole chamber.

I made a sufficient vitae-and-chunky-mors room, took stock of the range of timings I had available for assembly room, and then got completely stuck.  Assembly was the wall.  If I overlapped some bonders on the output it was a free 122c but that was obviously cheating.  After several hours of effort, I managed a 19r assembly, where the final bond needed everything to wait just one cycle to avoid collisions before it could start again.  At 131c, it was within a single digit of my goal of 122, and I put it down and worked on instructions for a few days.

I kept coming back to it though, certain that 18r assembly was out there, taunting me.  And so, the night before the deadline, I tinkered more, and more, until I finally found this assembly chamber.  It had a massive delay on the metal, almost as long as my original chamber allowed, but it worked at 18r.  I watched it run, finally happy.  126 cycles, 670 cost.  I had done it.

But I didn't remain happy.  My original input chamber was built to get metal out as quickly as possible, and had an obvious delay getting the fire out.  This new build order was limited by vitae.  I could definitely rework the input chamber, to save one, or maybe even two cycles.  Right?

All of my ideas ran out of space.  Until this one!  A hex arm to handle as many jobs as possible to leave more room for arm bases.  It would save one cycle getting fire to the conduit.  The problem with the hex arm is that the timing now becomes exact on the metal - if you grab copper one cycle too late then the hex arm carries iron to its demise.  Because I already knew the assembly chamber's required timing, I measured it out and was very fortunate that the "grab, 3 move, drop, 1 move reset" option aligned perfectly.  And after a little effort, the rest of the chamber came into place.  1 cycle and 100 gold later, I could rest.

Sitting on 18r with good-enough latency (it's no 122), I'm pretty confident.  The route to lower rate would be to put the quicksilver in the assembly chamber, move it to projector via conduit-swapping, and honestly that approach gets you all the way to input speed if it works.  But definitely there is not space for it.  Even adding a single arm to the assembly chamber I can't build the product in 18r anymore, so adding an arm and an input with strict timing, would hurt far more than it helps.

Curious to know if anyone out-sweated me this time.