It's a valid routingIt uses 15 of the allowed 16 segments (as you no doubt know already the LHR-LCY and MEL-SYD surface segments both count towards the total)

So you have one left to play with - ideas:

• start from somewhere else in South Africa (e.g. CPT-JNB...)
• squeeze in one more Nth American segment (you are allowed up to six flights in that continent)
• have a European side-trip - fly LHR-XXX and then XXX-LCY; airline route mapper shows a number of ports serviced from both LHR and LCY for example NCE and ARN - you could even transit through LCY and thus avoid the UK APD tax on the trans-atlantic flight(e.g. ARN-xLCY-JFK)