Would seriously doubt QF has two FC seats open for FFers on every flight. They only have 14 seats in the cabin and usually when I've flown QF on trunk routes such as LHR-SIN-SYD or LAX-SYD it is quite full with people waitlisted.
Would your group split up? One F traveling separately? Also check some non-trunk routings - SFO-SYD or LAX-MEL. I've also heard about people snagging J and F seats from JFK when there were no seats on the same day from LAX even though the plane goes JFK-LAX-SYD. The same thing happened to me years ago when BA flew SAN-LAX-LHR. Couldn't get F seats out of LAX but SAN was easy so I just drove down and picked up the SAN-LAX-LHR instead of LAX-LHR.
I think QF tries to allocate seats by gateway on a per week/month basis - not per flight. So check off travel days such as Tuesday or Wednesday going Down Under - because you loose a day these are low days for business travel.
In addition to JFK and SFO - also check out HNL - you could fly via IAH or EWR and connect to QF there.