So I have spent some time having a play this morning, and it seems that "computer says no" is the answer.
I put in your dates and ports (although I made the departure leg 28 April, as obviously it won't let me do last year!) and got this result:
- "lowest fare" economy - no
- "flexible fare" economy - no
- "lowest fare" business - yes
Which is exactly what you got - so the issue is
NOT the way you are searching, but seems to be as you said - either the fare rules don't permit, or QF IT does not permit the stop over. It also does not seem to be because you have already started the trip and are trying to change part way through, as it would not let me make a whole new booking. So as you have found details that the fare rules should permit, all I can suggest is keep trying to get a knowledgeable agent to help you.
Super frustrating for you.
I don't know if one of the more expert members like
@madrooster or
@Mwenenzi might have further suggestions to help you out. I'm just a keen amateur who goes to DXB a lot to visit family.
Sorry I don't have better news for you. And welcome to posting on AFF. Good luck and let us know how it all goes.