Your best bet is the QF F lounge via OWE. Assuming the lounge is open when you’re passing through, I’d do that then go direct to the gate when you get the boarding notification. TBIT to T4 is a 2-5 minute walk depending how quickly you move. There are times when AA uses the TBIT gates so you’d actually end up closer.

No need to hit the FL unless you need assistance with IROPS or want to plane watch, which is always nice at the FL.

W/r/t connecting through LAX — pre-COVID my HND flight parked at a remote stand. This could definitely be a thing of the past, but wanted to point out that wrinkle as DFW doesn’t have the bus situation.