that's an option, or potentially search CBR-NYC using flexible with dates for all flights option (ie: CBR-SYD. SYD-JFK) option, which should bring up the calendar view, then select Business class to bring up any options, which could bring up options with "Your flight from Canberra to Sydney will be in Economy" options.
Now I searched briefly Nov and Dec and only could find Premium Economy to get to New York, but it did give me an option for 132,800 points (plus $234) using QF/JL:
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The other thought that occurs is that you might want to search on CBR-SYD (or MEL) for the day before given US flights tend to leave in the a.m. in general so that only leaves the first flight or two of the day for reasonable connections (as above).
You might also want to consider searching on other options such as SYD/MEL-DFW-NWC (AA fly to EWR/LGA too iirc), MEL-LAX-NYC and potentially even things like options via HKG on CX and not to forget the QF AKL-JFK flight from June, but I suspect that will be nigh on impossible for J rewards.
good luck.