My wife has just got back from her award trip in J BNE-JFK and return.The award was via NRT and was booked 3 months out.There was virtually every day availability on AA JFK-NRT and some choice of days on JL BNE-NRT and QF NRT-BNE.No F on NRT-BNE and only old style J seating so better if you can get NRT-SYD for a better product(though not on the JL service).In 2006 both of us did this trip and had to route via SYD in both directions and use CX for SYD-HKG-NRT.
Obviously these are OW awards but have been organised with 3 and 6 months lead time and virtually days we wanted.Also as has been hinted at look at QF LAX-BNE or LAX-AKL then SYD or MEL.These are much more likely to have J availability for awards.