Part of this depends on the fact if JAL is allowed on your ticket or not. (Was your ticket issues before or after JAL joined oneworld?)

An alternative routing (with JAL) could be:

EZE-SCL-GRU-JFK-YVR-MEX-DFW-LAX-SYD-AKL-SYD-HKG-BOM-HKG-NRT-LHR-NBO

The YVR-MEX flight is only twice a week though, but there are lots of options to save segments, at the cost of real first class. (i.e. SYD-BOM instead of SYD-HKG-BOM, or AKL-HKG instead of AKL-SYD-HKG)