Mwenezi - great advice. I tailored your second itinery a little bit to go home via Madrid and it's all got the green light:

LHR-CMB,NRT-HAN,SIN-MEL,BNE-ZQN,AKL-SCL-GIG-EZE,LIM-UIO-MAD-LHR

Dr HFH - I've heard that the ticket will be cheaper avoiding Heathrow but I've not been able to find this using OneWorld's booking tool. I've tried using European cities and now Dubai on your advice as starting cities and can't get them any cheaper (even when completely avoiding London in the itinery) - perhaps I'm doing something wrong?