There are techniques for reducing the reserves needed to be carried by not initially dispatching the aircraft to the final destination. The mechanics are a bit arcane, but it's something to do with the fact that some reserves are a percentage of the flight time. So an LAX-NRT flight might be dispatched only as far as somewhere like ANC. Approaching ANC, calculations are done to see whether the fuel on board is sufficient to allow the aircraft to be redispatched for a "flight" from its current point to NRT. If so, the aircraft can continue. If not, the aircraft will make a tech stop at ANC to refuel.
NM's numbers raise another point, though. If you try to "squeeze" even a few hundred more miles from the aircraft, you are starting to leave pax behind at a rate of knots. If you reduced the payload to, say, 120 pax so that you could do LHR-SYD, that's all well as a technical possibility. Given that the costs of operating the aircraft are still of the same order of magnitude as when it has 250-300 pax on board, you are basically looking at an all-business class (or higher) configuration. The service would just be not economically viable.
The ultimate demonstration was that QF 744 delivery flight non-stop from LHR-SYD. To get into the appropriate record books, it carried something like 5 pax. Even then it was touch and go whether or not it was going to make the entire flight. I wouldn't like to be one of 5 pax being charged a commercial fare for the trip.