SYD-DFW via ?
What about 1 stop to DFW but not via LAX, SFO or HNL
Great Circle lookup shows that SYD-LAX is 7488 mi but NAN-DFW is 6625.
The American's love Fiji, they love all of those overpriced 5 Star resorts near Nadi. Gee, you could set up a 'golden triangle' for the cashed up Americans with say AKL & BNE with a partner like Air Pacific, then back on QF from NZ to OZ or make their own way to SYD if arriving in BNE, who knows, it might work???
Then back on the 1 stop SYD-DFW service, avoiding LAX but still partnering with AA from DFW to other points in the US of A.
But that won't happen - as per last line by RedTBar above.