I tried for way too long at period 4, eating up the better part of 4 days.  This is not optimized well at period 5, it just reflects me giving up on period 4 but wanting to have something better than my cycles solve.  The crucial thing that period 5 unlocks is the ability to spin the triangle over the triplex and output in the way done here.

See my showcase for a very similar period 4 near-miss that just needed to place one arm outside the left cabinet.