and the verdict...
JL wins on the ORD-BKK segment. Just changing that one segment off AA (and the AA codeshare with JL to BKK) made a
$2800 difference in the fare, dropping it to US$4300. Of course, that means no status points on AA, no double miles, and no use of VIP2 to upgrade to first

but such is life.
So
ORD-BKK on JL
SIN-MEL-OOL (Gold Coast, actually closer to where I'm going) on QF
OOL-SYD on QF
SYD-LAX on AA codeshare (QF metal)
LAX-ORD on AA
Amazingly, this is $46 cheaper than the cheapest ORD-BKK full J-class fare alone!