Clearly you could do a load better on miles.

1) Use all 16 segments (some error regarding Tokyo. CX only flies scheduled flights from NRT)
2) Fly to the opposite sides of the US - so do East Coast to Asia and from LHR to West Coast.
3) Don't use two segments to get SWP-Eur, use one (enter SWP from as far north in Asia as possible: HKG, or even NRT)
4) Try to avoid very short segments like LAX-SFO

To take part of it as an example:

SFO-NRT-HKG-SIN-SYD is 12461 flight miles
SFO-HKG-SIN-NRT-SYD is 16684.