Actually you could do PPT as part of a Oneworld award; since the distance is only calculated from stopover points, you could do:
DFW-LAX-HKG-BKK (as close as you can get to HKT on oneworld metal).
BKK-SYD-SCL-PPT
PPT-SCL-DFW
for 120k each in economy or 150k in biz class
Or Australia:
DFW-LAX-HKG-BKK
BKK-SYD
SYD-LAX-DFW
also for 120k/150k
Hawaii would be slightly cheaper at 100k econ/130k business
DFW-LAX-HKG-BKK
BKK-SYD-HNL
HNL-DFW