Help with booking a itinerary for maximum status credits

I need to book a trip in August for work which will take me from Melbourne to London, Toronto and LA before returning to Melbourne.

I work for a NFP and normally we would book via our travel agent and would be given the lowest possible fare on any carrier, but I have some vouchers which I need to use up from Qantas and given I am donating them to work I have been given approval to book direct from Qantas.

I currently have PS with Qantas and would like to keep it. I normally between work and personal flying have been able to scrap in keeping my PS and enjoy the free seat selection. I also have a QP membership into next year which has me happy to fly what ever stupidly long route required as I can relax in the lounge.

My question is, is anyone a guru here and able to advise me what the best route to take from Melbourne, to London where I will spend a week (18 Aug - 24), then onto Toronto for another week (24-29th) and to LA for a week (29th - 3rd Sept) before returning to Melbourne.

Having a look currently the best status points route I found was MEL-SIN-DXB-LHR then LHR-YYZ then YYZ-LAX then LAX-BNE-MEL but I am by no means a guru at this and would love any suggestions on how to maximise my status points for this trip.

thanks in advance

 

Unfortunately we are not allowed to fly anything other than discount economy, even our CEO does given we are a not for profit.

The route above I researched is on QF flight numbers excluding the legs between London/Toronto and Toronto/LA which are on BA and AA flight numbers.