I don't think you can come remotely close and keep it mostly in F. You can do a lot better on AONE5 or try this AONE6 for almost all F
MIA-ANC
ANC-DFW
DFW-JFK
JFK-LAX
LAX-SCL
SCL-IPC
IPC-SCL
SCL-LAX (or MEX if you want BA)
LAX-LHR
LHR-MCT
MCT-LHR
LHR-MRU
MRU-JNB
JNB-HKG
HKG-NRT
NRT-DEL
DEL-HKG
HKG-SYD
SYD-JFK
Just retweak the ANC part for the winter season. That one is 76497. (not sure they'll let you transit lax back from scl, mex gives 75100)