First up - understand that you can either have an en route stopover or an open jaw, but not both.
Departing from BNE and returning to SYD will create an open jaw, which means you can only have one stop overall when overseas (i.e. your "destination"). So you will be better off departing and returning to the same point.
As it stands - let me try and decode this - you want:
Brisbane (BNE) - Zurich (ZRH) [stop 3 nights here] - London (LHR) or Paris (CDG) [stop 3-4 days here] - Newark (EWR) [stop 6 days here] - Brisbane (BNE)
No can do this - you are trying to have 2 en route stopovers, you can only have one. As it stands, you'll need to choose whether you want to stopover in Zurich, London or Paris. You fly to that stopover, do what you want in Europe, then pick up your itinerary again to fly onto Newark. (I recommend Zurich or Paris; if you choose London, you will have to pay the UK Air Passenger Duty, increasing the amount of taxes you have to pay).
I just booked a similar itinerary for my folks. Their en route stopover was London; their "destination" was EWR; origin city was BNE. They returned to Australia via Europe, and that was purely due to timing and seat availability. The only other option to return home not going via Europe was to travel from America to Asia direct (e.g. Chicago to Seoul), then back to Australia. Availability of seats from America to Australia crossing the Pacific was almost nil in J and F, across all carriers. And just for the note, my folks depart in August and return in September.
