Electronic – Gain vs Output Impedence

The problem in your design isn't the output transistors and neither will this be solved by using darlingtons - in fact the problem will become worse with darlingtons. Look at the spec of the NE5534 and read the section about maximum output voltage swing.

On page 5 it tells you that the max swing might be as low as 24V on a +/-15 volts supply i.e. a 30V supply only guarantees an unclipped output swing of 24 volts p-p - that means the internal transistors in the device "lose" 3 V top and bottom. This doesn't magically improve on a lower supply and you should expect, on a 9V supply, to generate a maximum output swing of 3 volts peak to peak.

OK, if you used the typical spec of the NE5534 this might rise to 5 volts p-p.

This is then compounded by the push pull stage - it's an emitter follower push pull stage and it's output will "lose" between 0.6volts and 1 volts per transistor depending on your load.

This leaves you with a crappy 1volt to 3.8 volts p-p being fed to your headphones before clipping takes place. If you use darlingtons, they "lose" double what a regular transistor loses so this will be even worse.

Recommendation - use a rail-to-rail output op-amp. There are plenty around these days and they'll probably only drop about 100mV per rail.

Pretty much the normal rule is that the output impedance is the bias resistor. This is because the output is usually a jfet's drain and in normal bias configurations for a jfet it operates as a high compliance output hence output impedance is largely dictated by the external bias resistor.