The Green Goblin.
You may be surprised to learn both Airbus and Boeing build ultra long range aircraft as per the current definition.
In the case of the Airbus it (A340-500) has not been been successful due to the payload/range/fuel chart. SQ are the only ultra long range operator (SIN-JFK-SIN) with 100 J class seats.
The B777-200LR Worldliner can carry 300 PAX LHR-SYD or LHR-MEL nonstop in a 3 class configuration. Westbound with a full load a technical stop could be in either PER or DRW for fuel and crew change.
I would see this service with First, Business and Premium Economy Pax as the only way QF could compete with the Middle East carriers. In the event of hostilities in the Middle East or a swing away by Pax from the Muslim Middle East carriers QF would be in a box position.
OMG, I have forgotten one thing. Boeing offered to build a 'special' QF B777-200LR model a number of years ago for SYD-LHR using some B787 technology such as B787 shadeless windows etc etc but it was turned down as old technology.
(Boeing built the B747-400ER especially for QF and who are the only operator of the model)