When I mentioned "balanced output" I was referring to the analogue cable I'm using to connect the headphones to the DAC. Balanced means you get separate channels for each ear in your analogue signal path.
With a Bluetooth connected wireless headphone, it's always balanced by definition. But when I said "that kind of sound quality isn't possible" with Bluetooth, I was referring to a different problem: Digital to analogue signal conversion.
In my setup, it happens in the DAC which is audiophile quality. Signal path: PC - (digital USB) -> DAC -> Balanced cable (analogue) -> Headphones.
In Bluetooth, it looks like this: PC - Bluetooth (digital) -> Headphones (which do the digital to analogue conversion).
This signal conversion can't match the quality of a dedicated desktop DAC.