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That changes everything

The 470 ohm resistor will limit the power into the headphones and will make the power delivered less dependent on the headphone impedance. If the headphone impedance was 470 ohms also then half of the power available would be dissipated in the resistor and half in the headphones. For the 300 Ohm HD600 the 9Vrms available will now become 3.5Vrms due to the potential division of 300 and 470ohms (9 * 300/(300+470)) and so the power reduces from the 270mW originally calculated to 41mW (by V^2/R)
For the 20 ohm headphone case the voltage is reduced to 9V * 20/(470+20) = 0.36Vrms and the power becomes 6.6mW (down from 4W!). Again, how loud the headphones go depends on their sensitivity.

Another factor is the source resistance seen by the headphones. If the headphone impedance is not flat with frequency then there will be a non-flat response curve. Damping factor may also play a part - not sure how important it is for headphones. Benchmark media have written several white papers about, in their view, the importance of driving headphones from a low source resistance.


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