Update: Still having an issue with the headphone out. I was fooled into thinking that the issue was resolved because of the behaviour of phones output.
If the phone output dial is set to just below 9 o'clock, the left and right channels are balanced and sound ok. And here's the unexpected behaviour:
If the the output dial is turned all the was anti-clockwise (about 7 o'clock) then the left channel has no output, as expected, but the right continues to have some output, albeit reduced in volume. If the output dial is then turned clockwise, to about 2 or 3 o'clock, the left channel's output increases normally without distortion, but the right channel's output increases at a lesser rate and sounds distorted and crackly.
Confirmed this behaviour with 3 headphones. Ideally, there's solution, but I can live it if I limit myself to using the headphones with the output set just below 9 o'clock.