Well, surprisingly we've had a resolution for our JQ Japan itinerary. We've had countless phone calls to both Qantas and Jetstar, messages to Qantas on Twitter, a compliant through their website and a subsequent ACA complaint.
At some point during all of this, someone was able to rebook the JQ flights and make them stick (no one seemed to know how), but Jetstar still needed to be "paid". Our points had been taken, however our visa card payment (for taxes) had since been cancelled after pending for over a week.
We were advised that they could not take this visa payment again without also deducting the points again, they couldn't deduct the points again because we had an insufficient points balance. The points couldn't be refunded unless we agreed to cancel the entire booking, but if we did this we couldn't rebook because the reward flights were no longer available! Frustratingly, the agent did not seem to understand this paradox...
I ran the usual speil - "Can you please escalate?" "Can I please speak to a manager or complaints department?" etc. This was all rejected by the agent as not possible.
So, I tried another option - I simply asked for my call to be transferred back into the queue for a new agent. Another 40min hold later and I had a new friend to tell the saga too (I was getting pretty good at it now). Believe it or not, he just asked to confirm my visa card details and 10mins later sent me my ticketing confirmation.
I couldn't believe it... I told him just how much of a legend he was! He seemed so genuinely shocked to receive thanks, completely breaking character from the standard monotone call centre voice..
I was actually worried that he was tearing up a bit. Just imagine what it's like to work in a Qantas call centre right now?!
I hope anyone else that comes across this thread because they're in a similar situation gets their issue resolved as well. It won't be easy, but once it's done you can promise yourself to never fly Qantas again (once your FF points run out at least).