If you don't need to be in SIN, then you may also want to consider using CX via HGK. Some regulars around here (eg number_6) tell us that CX is the leader in F service presently, followed by QF with BA coming in last. I can't vouch for it as I have not travelled BA or CX in F, but I do greatly respect number_6's recommendations.

Also, the CX Wing lounge in HKG is fantastic compared with the BA/QF F lounge in SIN. But I do note you have some other CX F flights included so I expect you may be keen to sample the F product of some other carriers as well as CX.

The benefits of splitting LHR-MEL into two sectors are really based around the tier credit mechanisms used by BA and QF. Note that some agents will tell you they cannot sell you LHR-SIN-MEL on the same flight number on the same connection and have to sell it as LHR-MEL instead. I got around that by telling agent to leave me in SIN overnight and book me on the SIN-MEL flight the next day. Then after starting the journey I called the airline to change the date of the SIN-MEL sector to the same day as I arrive LHR-SIN ... so I have the split routing all on the same flight which helps for my QF earning.

I am going LHR-SIN-MEL on QF since I earn more on QF flights than CX flights via HKG. I am in J, but if travelling in F I would be taking the CX recommendation and forgoing the extra QF points.