As a Sydney boy living in Europe for the past 12 years, and making the trip home on average twice a year, I've tried just about everything. Like you, my main priority is keeping the journey time as short as possible. While there are variations of an hour or so on the flight times of the different routings (the main variants being via SIN/KUL, HKG or DXB/AUH), it is the connection/transit time that makes most of the difference. Another factor to consider is how long you'll be waiting for the next flight if you miss a connection or there's some other problem with your originally booked flight.
My knowledge is a little dated as now that there are several long-haul options straight out of GVA I never go through LHR anymore. But I would summarize your options as follows:
SQ: pros: good connections, several flights a day, excellent service, SIN is good for transit. Cons: no PE, J class at the nosebleed end of the price spectrum.
QF/BA: steady and stolid, mediocre in every respect but will get you there in reasonable comfort. Generally good connections (although now somewhat reduced). PE available. But both PE and J way overpriced in my view. May be worth waiting to see what offers come up when the QF/EK tie-up is finalized in March.
CX: excellent connections, convenient schedules, good service, HKG convenient for transit. Would be my pick for PE; sometimes good J deals.
EK: shiny planes, generally good service, reasonable connections. Very nice in J, but no PE. Sometimes good deals in J (but seems to be getting rarer). Big con: DXB is bursting at the seams. Even the J-class lounge is like a human tide at peak times.
EY: my current favourite. No PE, but often keenly priced in J. Not sure what the connections are like from LHR (it's currently the fastest route GVA-SYD). Lovely service, genuinely friendly. AUH not great, but much more pleasant than DXB.
MK and TG: Fine when things go well; a nightmare when they don't. Can be very good value in J, but somehow never are when I need to travel. I wouldn't use these for a short visit of two weeks, as you risk losing a day or two if things go wrong.
I haven't tried Virgin - that would be your only other PE option I think (unless you are willing to add a stop in Europe, which opens up many other possibilities).
The last time I was in Oz, China Southern was heavily promoting its new SYD-LHR route via Guangzhou. No idea what the connection is like, but if it's good it might be worth checking out for cheap J-class deals.