Thanks for the tips. I modified the ITN a little bit and changed the direction also, this should now, to my understanding, apply to all OWE rules and also use every segment allowed.

CAI-LHR-LAX-SJU-DFW-YVR-DFW-CUN-JFK(-YVR)-HKG-BOM-HKG-NRT-HKG-AKL-MEL-PER-AYQ-SYD(-BKK)-LHR-CAI

Any comments & suggestions still most welcome!