Gosh height>cycles has been a fun time. My first solution draft took just over 120 cycles, operating at 20 rate. I managed to make some marginal improvements over the course of the first day, ending with a rate 16 latency 25 solve for 105 cycles. 
I then decided that was a good enough draft, and started working on an actually good submission. Min rate is 6, but then I'd have to somehow slide some duping bits past my input, or else slide all my products past a berlo wheel. Thus I decided to get as close to rate 8 as I could. My first method ended up as a rate 10 latency 49 solve for 99 cycles, only saving 6. After a large number of tweaks, I managed to remove 10 latency, ending up with an 89. At this point, nothing appeared to be improvable, as multiple arms were using the full rate and there was no space for new arms to help them.
But then, one by one I found ways to work just a little faster. The final construction couldn't be sped up, but a bit of rearranging let 2 arms handle it instead of one. I split the work of the arms moving from the brick to the construction site differently, taking them down to a 9 cycle loop as well. And finally, I redesigned the entire duplicator setup on the left to get arm 9 operating in a 9 cycle loop. Almost every individual piece of the solve works differently, and yet the atoms move almost the exact same way. And somehow, this saved 3 latency too. Not entirely sure where it went.
Try as I might, I can't see a way for this design to reach rate 8, since doing so would require an entirely new method for offloading the water from the input, and would therefore likely have a completely different brick structure.

Yes arm 9 does break height 4 literally one cycle later in order to loop, what about it