How to upgrade Melbourne to Europe Emirates flight using Qantas points?

I have booked a QF trip on Emirates in August, for me and my partner -
Melb - Paris - 21 Aug - QF8407. QF8073
Lisbon - Melb - 16 Sep - EK192, QF8408
Booked under code “Q”, which seems to be ‘discount economy’ - not sure if it is ‘sale’ or ‘saver’ in respect to change/cancellation fees …

I’ve decided I really want to treat my partner to a business upgrade, if there is any way my budget and points can stretch.
Can anyone advise on what some of the cheapest options might be to do this?
Qantas tells me my fare cannot be directly upgraded.

Happy to just fly the Melbourne/Dubai legs in business, and fly the rest in economy.
I have about 221K points, and my partner has around 50K points.
My partner is Silver, but Ive recently been bumped back to bronze.
I don’t have a business credit card unfortunately, but I have an ANZ black and AMEX ultimate.

Is there anyway backdoor way I can upgrade with Qantas or Emirates?
Would I need to cancel and rebook with another non-Qantas carrier?
Are there any other travel agents that specialise in finding sneaky ways to get cheap upgrades?

I looked at IflyFlat, and similar sites, but they seem to require a higher minimum number of points…
I also joined Alaska airlines with the idea to buy points, but it seems as though the points qantas required for business fares are quite astronomical …

If anyone has any tips that I haven’t thought of (other than just pay for 2 business flights that I cant afford) I would be very appreciative, as I’m quite new to this stuff.

You can't upgrade those flights with points (Qantas, Emirates or otherwise) or money unfortunately.

If you want to fly business you’ll have to cancel those flights and re-book (eg flying Qantas via Singapore/Perth and London), though in peak season as a silver it’s a real gamble to try to get an upgrade that way.

You may have some luck if you fiddle around and look for indirect flights on other Qantas partners that aren't bookable online, you could try calling Qantas and hope you get someone patient. Otherwise book a cheaper business class flight, like Vietnam Airlines, Royal Brunei, Scoot etc.