Contact consumer affairs in your local state. They offer free advice and guidance on consumer issues.
You are covered under consumer law, and not receiving the product you paid for gives you the right to a full refund. Transferring to Qantas economy class does NOT waive those rights (if they had accommodated you in Qantas business class you would likely have little or no recourse).
Not sure if you had the opportunity to keep your Qantas economy boarding pass? or at least take a photo of it? That would have been immediate and irrefutable proof. However, if you don't have it, not to worry. You'll be able to get details from Jetstar about where they ended sending you (ie, to Qantas, economy).
This could take time, and a bit of back and forth, but you will get your full refund. It just needs to get before the right person at jetstar. Dealing with frontline customer service may not get you the right result (if it does, bonus!), but eventually it'll make it's way to someone who knows what they're doing.
This is totally a Jetstar issue. Qantas has nothing to do with it - so don't let Jetstar fob you off.
As to the interaction at the airport, after Jetstar cancelled, they transferred your ticket over to Qantas. At that stage, in the eyes of the 'unhelpful colleague' they will have seen your ticket is with qantas already, and they were probably right that Jetstar, on the spot, probably couldn't arrange to refund your money (because you no longer had a ticket with them, it was now with Qantas).
However, now that the date has passed, this is entirely for Jetstar to sort out. You don't need to deal with Qantas, only jetstar. Show them your original ticket in Jetstar Business, say that the alternative on Qantas economy was not acceptable, you chose not to fly, and now you would like your money back.
I'm not sure if you will get any compensation flying Thai economy, or even the difference in fare. This is because if you were able to fly Thai economy, you would have been able to fly Qantas economy. Which then makes the transfer to Qantas a fair and reasonable option. BTW, the layover in SIN was probably more than enough time. The mimimum connecting time there is pretty short, less than an hour.
If you need to, you probably could end up disputing with your credit card, but try the above first.