I guess it boils down to transpacific F on AA v. J on CX. I'd pick CX and go EZE-SCL-LAX (LA) - HKG-DEL (CX), or just EZE-JFK-HKG-DEL. I don't think there's a prohibition on openjaws on your no-stopover transit through NA en route to Asia, so if you want to pay for the segment, you probably go EZE-DFW//ORD-DEL if you can make it all in less than a day.