Chris, there's little I can add to your superb demonstration. The only additional factors are often driven by the 'bean counters' that prevail in any airline operation. They would see the opportunity to carry passengers between the refueling stop(s) and final destination that might not otherwise travel beyond those points. Somewhat akin to you Brits travelling from London to many of the Cairbbean or Mexican east coast destinations being required to land in Ft. Lauderdale or Miami. BA can, without violating ICAO cabotage rules, pick up additional passengers on the Miami to Barbados leg(as example).
Additionally, flight crews can only be on duty 14 hours and accumulate 10 hours of actaul flight time(as a general rule) within any 24 hour period. Long haul's require carriage of additional crews in sleeping quarters that take up a lot of valuable passenger revenue space...
Finally, as many airlines transition to more fuel friendly, large two engine aircraft as opposed to 4 engine (the venerable MD-11, DC-10 and Boeing 727 have been or are being phased out) the ETOPS rule becomes more noticeable. Stands for Extended-range Twin-engine Operational Performance Standards which says that a two engine aircraft must never be more than a given, proven time on one engine from an adequate landing site. Most airlines start out at 90 minutes and progress up to the now average180 minute standard. A lot of money invested in training, navigation standards, engine monitoring and other factors is required to extend that time by any appreciable amount. The rule doesn't apply except to two engined aircraft...