Trackless rate makes my head hurt.
I hesitate to call this optimised, but it's much better than my first attempt.
Grab-rotate-drop arms are a godsend.
Sticks make timing the outputs easier, a bit.
Found some lucky geometry for the output.
Somehow there are no collisions, magic.

Wish I'd realised in advance that you can't have two hexarms deliver to one output on a four loop, because you run out of chances to output the third pipeline. That was a nasty surprise.