It came down a lot from my initial 2-arm solution.  I got 221 cycles with 2 arms and it stayed my best for quite a while with 442 tarcles.  Then I finally got into the sauce with this length-2 hex arm grabbing earth.  At first it was around 450.  My goal was something like 3 arms 120 cycles but I kept needing either an extra arm or a long period piston.  The breakthrough was the ability for the length-2 hex arm to reorient the extra piece.  That immediately improved the period from 20 down to the minimal 17 given this process, and amounted to 60 tarcles from 399 to 339.  A couple more latency later to this and I could believe I'm at global min.