From the very beginning, I made a simplifying assumption.  Read the molecule clockwise along the bonds.  The atoms have to go through the conduit in that order.  Left chamber would be dedicated to getting the atoms through the conduit in that order no matter the bonds, and right chamber would be dedicated to reassembling it.  This converts the bond information into timing information.

In my speedsolve, this was done using several different drop instructions over the conduit, and the solution was 1P.  But I wanted to find a 1/6P approach, and I dreamt up the right half to support it.  It builds a complete bonded triangle, but depending on when it gets its last atom it will break a different bond.  Then the helper arm will spin it into the proper orientation based on the same delay tactic, and finally a timing arm will be the one to do the output.

The right chamber was built first, and the left was built to support it, gradually dropping from 17 instructions down to only 11.  Once I saw how simple the 11 instruction left chamber was, I doubted the right chamber's performance.  But when I tried to build "the left chamber but in reverse" it didn't exactly work..