Here are three possible iteneraries. The first one is a LONE5, the second two are LONE4 which skips South Africa to save money.
LHR-DOH,CAI-MAD-RIO-SCL-IPC-SCL-AKL-SYD-CNS-PER-NRT-TPE-HKG-PEK,DEL-HKG-JNB-VFA-JNB-CPT-LHR
LHR-DOH,CAI-MAD-ACE-MAD-RIO-SAO-SCL-IPC-SCL-AKL-ZQN-SYD-CNS-PER-NRT-TPE-HKG-PEK,DEL-HKG-LHR
LHR-DOH,CAI-MAD-ACE-HEL-NRT-TPE-HKG-PEK,DEL-HKG-PER-CNS-SYD-ZQN-AKL-SCL-IPC-SCL-RIO-SAO-LHR
Let me know what you think! I'll try to book one of these soon and let you know how it goes (especially since the open jaw thing is somewhat iffy). By the way, both Mileage Monkey and the oneWorld desktop tool state that there is no oneWorld service between the Canary Islands (ACE) and Helsinki but I found some nonstop flights. Any thoughts on this?