You have the theory of operation correct so it should work. All parts go together dry, except for the main spring, #7 and the cup, #9, which should be lightly greased. A common mistake is not getting the hook on spring #8 placed correctly over the vertical tab on the cup, #9.
As the rope is pulled and the starter pulley, #4, starts to turn, the tension of spring #8 holds the pinion gear, #5, in place and it starts to climb the threads on the starter pulley. If the pinion gear spins with the starter pulley instead of climbing the threads, I’d say there isn’t enough tension on the #8 spring.
What shape are both threads in? Any nicks or rough surfaces causing the parts to bind?
