Just as an aside regarding a stopover, on such ultra long flights surely a few hours to stretch the legs/let the lungs breath good air would be of benefit ? The Singapore stop would allow a nice few hours to wander around the city and have a nice meal etc. Obviously Dubai is a matter of (bad?) taste, LAX only a humiliating 'transit', so perhaps no chance/desire to do a stop there.
Maybe a discounted round the world ticket in business might be as cheap and perhaps routable via Vancouver ?
SHJ