This arrangement seems to work well in terms of audio quality
Is there a better way to achieve this minimalist approach, (single component audio amp),
I've seen a lot of other comments about using a mosfet instead of a darlington, but is that not an appropriate application for my purposes?
The thing is that you can not expect to have a single component amplifier. About the best you can do is use this poor, but not utterly crap circuit:-
that circuit might require a darlington configuration for some relatively substantial power handling, right?
If you put a darlington into that circuit then the biasing is all wrong so you need to adjust that. Also I believe that the gain would be too high and you would not operate in the liner mode. The power transfer between speaker and transistor is via a 10uF capacitor that would need increasing. Finally the 1K collector resistor means the transistor is not going to draw more current than 5mA anyway.
Is the reconstruction filter something like this?: