OP If your purpose is to gain miles, then your itinerary
> TXL-LHR-AUH-NRT-HKG-SYD (or MEL) LAX-NYC-TXL
is not particularly efficient... for starters you aren't even close to using all 16 of your allowed sectors. You could do more flights with no increase in base ticket cost and only pay extra taxes/fuel surcharges.

Since you are flying LHR and to SYD, if you don;t need to stop in Japan before Sydney, you could fly the Qantas LHR-SYD or LHR-MEL flight which is a single flight number and only counts as one segment. That is a lot of miles for one segment.