So I tried my luck calling the 13 12 11 number (instead of the normal 13 13 13 number) and it appears that I got through to a premium line even as a lowly Bronze member!
From the personnel's accent, I assume that they were in the Auckland office.
Very helpful - was able to see the requested flight / seats immediately upon giving the details (not the usual "we can't see that flight / seats", "those seats are available for new bookings only" etc).
Got the change done to a day earlier and they called back approximately 45mins after the call to confirm it was all done, I've logged onto the Royal Jordanian MMB portal and the new e-ticket numbers are there!
No change in points (still 318k) but just $17pp in extra taxes. Happy days.
I know it's pretty sad to be excited about such a simple change being done successfully, but that's Qantas for you!
Bottom line - try calling 13 12 11 instead of 13 13 13.