Just being able to fly a route with a load of passengers does not necessarily make it viable from a financial perspective.

Before the 747-400 was available, the only aircraft that could fly reliably (well, reasonably reliably) trans-Pacific between LAX and SYD was the 747SP. QF did quite well on this route with the SP since they could operate with a reduced economy cabin and more F/J seats, and charge a premium fare for the benefit of a non-stop service.

However, once the -400 was available, it cost about the same (from an operating perspective) to fly a SP on the route as it did to fly an -400. But the -400 could carry a swag more passengers and even a little cargo on the eastbound services.

The really long flights where the aircraft is weight restricted are very marginal from an economic perspective. Unless the operator can charge a significant premium for the non-stop service, its not going to work. And the only people willing to pay more are the premium cabin travelers. Discount Y passengers on their once-in-a-lifetime holiday don't mind the midway break.

So it is much more economically viable to leave LHR with up to 284,400 lb of fuel onboard your A340-500 and fill up to the 804,700 lb MGTOW with pax and freight. Then stop somewhere in Asia to drop/collect passengers who are willing to pay 70% of the LHR-SYD fare for 50% of the distance, as well as drop/collect freight, top up the tanks and head on down to SYD.

Based on this analysis, and the fact that freight does not complain about a short refuel stop, don't expect to see too many A340 freighters operating. The ideal freighter is one with a very large spread of Empty Weight to MLW. Then the spread of MGTOW to MLW dictates the fuel that can be carried and hence the range for each sector. Based on this, the 747 and DC10/MD11 make better freighters than most Airbussen.

As for aircraft that will possibly be seen on the ultra long-haul ops, yes the A340-500 is one, also the 772-LR and the A330-200. EK have just started A340-500 ops DXB-SYD, scheduled for 13:55 non-stop operation. But if BA were to consider LHR-SYD (or LHR-PER) non-stop, then I would expect the 772-LR would be more attractive as it would give some more fleet commonality, albeit with a new engine type as the GE90 is needed to get the max range out of the 777, even though the install set is about 6000 lb heavier than the RR Trent 800. But with QF going for A330-200 and -300 and ordering A380, they may find some reason to look at the feasibility of Australia/Europe non-stop with an Airbus.

The A340-500 is still heavier than AB would have liked. They really suffered with the A340-300 not meeting its design specs due to being over-weight and under-powered. They had to settle for second choice engines when the original engine supplier could not deliver.

The early A340's also suffered from poor climb performance and lower cruising speed compared with Boeing aircraft (747, 767, 777). This was a problem when leaving some Asian ports (as found by SQ and CX in particular) where route congestion means that unless you can get up high quickly, you will be left to cruise at lower than optimal altitude since everyone wants to be up around FL350 and above, but those levels are often taken by the Boeings that can climb to cruising alt at pretty much full weight, while the AB's need to burn off some fuel before they can get there. So the combination of less power than AB desired, slower cruise and forced lower cruise alt often resulted in less than desirable range and less than happy operators. But the A340-500 and -600 are supposed to overcome the well known short comings of the earlier models.