Was able to get LAX-MIA-MDE with 77W lie-flats on the LAX-MIA-LAX legs next May for $632. Might use a BusinessExtra upgrade to move into F on one or both of those legs as there is upgrade space available on them. Have never been to the QF First lounge at LAX, would be a good chance to visit.
Thanks very much MightyTravels, this was a great find, much appreciated!