Whilst re-timing DXB/LHR flights could work (and hence reduce some downtime), I dont believe re-timing LAX flights will. Firstly, assuming QF12 becomes a day departure, it would have to leave in early morning and this eliminates connections & feed at LAX. Secondly, off my mental calculations, it would have reduced connections in SYD - If it left LAX at 9:30am (which means it would need to take QF107 SYD departure time), it would probably get into Sydney around 7:30pm +1 day. Whilst it does give QF some lee-way, if it was 2hrs late, they would be over-nighting some customers. I also understand QF does some maintenance at LAX - so its not all wasted time.
I like the idea of a day-flight back. But I would suggest the 380 is the wrong plane. If QF ever gets them, the 787 may be the better plane to turn-around for a day flight... but there would still be risks.
I do like nighttime departures for QF 1 / 9. Whilst it would impact on LHR bound J passengers, it does open up better connections to EK's other European services.