Thanks for the all the advice and great links!

I did some more research and I'm curious if this would work (BTW - I'm in economy). Since I'm technically starting from the US, I'm looking at getting a flight to London and starting from there:

LHR-BOM
BOM-DEL (surface)
DEL-BKK
BKK-HKG (surface)
HKG-AKL
AKL-SCL
SCL-EZE (surface)
EZE-LIM
LIM-MEX
MEX-DFW
DFW-SJO
SJO-GUA (surface)
GUA-LAX
LAX-LHR

I know that I'm much closer, but would this actually work?!