I would probably stop in one or both places I mentioned, and more. But not a primary destination for this journey. Not that this matters other than for segments
I only put HND in there as I thought Japan would be a good stopover point as I love visiting there plus a Oneworld hub. The new A350 biz cabin is tempting too. Similar with SYD. A place I enjoy and another alliance hub.
I tend to default to Qatar flights based on past experiences. While researching this I had thought QF flights had higher fees, but both QF routes you mention would be unique in my flight map and the JFK flight would certainly qualify in the arbitrary “fun” category in my head.
My understanding for an AA 001 ticket only BA carrier surcharges are charged.
My understanding for an QF 081 ticket QF & BA carrier surcharges are charged. The online OW booking tool often defaults to QF ticketing
[but may be incorrect]