Here's a route that starts in ARN but uses LA's remaining F services in Latin America and across the Pacific; it avoids NA altogether, but includes Easter Island, one of those places where the OWE comes into its own. Bumps up to 10/20 in J, but that's the price you pay for exotica. You could include Moscow en route to ARN or as a side trip.
ARN-MAD-SCL-IPC-SCL-EZE-SCL-SYD-ZQN-SYD-CNS-MEL-HKG-NRT-BKK-HKG-SIN-LHR-DXB-LHR-ARN