Option 1
5 Cont F ex-YYZ 73594
YYZ-MIA-DFW-YVR-JFK-DFW-LAX-SCL-CCS-SCL-EZE-JFK-MAD-ATH-LHR-DXB-LHR-SIN-BKK-HKG-CEB-HKG-AKL-MEL-PER-DRW-SYD-JFK

to max mile LAX-(GIG?)-SCL-CCS-SCL-EZE-JFK-MAD

Option 2
4 Cont ex-GIB 66877
GIB-LHR-DXB-LHR-SYD-AKL-MEL-PER-SYD-JFK-YVR-DFW-PDX-DFW-LAX-JFK-EZE-SCL-CCS-SCL-MAD-LHR-GIB

you have too many segments in europe.
(LHR-SYD is okay as long as it is the same flight #, and therefore 1 flight coupon, i think it refuels at BKK/SIN)
you still haev 2 transcont JFK-YVR & LAX-JFK, you can change LAX into MIA or SJU.

an example will be
GIB-LHR-SYD-AKL-MEL-PER-SYD-JFK-YVR-DFW-PDX-DFW-(sju/mia)-JFK-EZE-SCL-CCS-SCL-eze-jfk-MAD-ath-LHR-GIB

Option 3
4 Cont F ex- YYZ 66315
YYZ-DFW-SJU-JFK-HKG-DPS-HKG-BOM-HKG-AKL-MEL-PER-(drw)-SYD-LHR-ATH-LHR-DXB-LHR-LAX-SJU-DFW-YYZ

Option 4
4 Cont F ex BKK 64622
BKK-HKG-DPS-HKG-AKL-MEL-PER-SYD-MEL-HKG-JFK-LAX-IAD-SJU-DFW-PDX-DFW-FRA-MAD-LHR-DXB-LHR-SIN-BKK

i am not sure if this one world, i think you might have to go directly from SYD to JFK (i.e. cannot transit at HKG). again JFK-LAX-IAD is 2 transcont. need to remove one

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i dont think there is need for advance purchase. you can begin talking to AA RTW desk to make reservation now, i believe.
(and use the software from cx.com or aa.com to get the schedules).
the most efficient way is to write down you preferred schdules and fax to AA RTW, and call to follow up.