Thanks for the replies.
PRR: I'm a bit lost how the capacitor in the power supply mitigates the resistance. As far as I know (consideration of the time constant) a 22uF cap does almost nothing wrt DC voltages while a 220uf cap "holds up" for about a millisecond. Great for ripple and grounding guitar frequencies but not buffering a supply with resistance. But I'm a complete beginner, and have a feeling that I'm about to learn something !!
I'm also wondering how the output of an LM386 can swing 6V from a 9V supply if there's "60 ohms" of resistance in the LM386 and associated bits and pieces. The datasheet for the LM386 shows a push-pull pair with no emitter resistors. In my simplistic view, I assumed it could swing almost rail to rail because there's almost no internal resistance.
So my thoughts when making the first post: I made a wild guess that adding 8 (or a bit more) ohms of battery resistance dissipates as much power as 8 ohms of speaker impedance (for the first 8 ohms). ie roughly 50% less max power. 24 ohms might give a 75% reduction in power.
e.g. from 1 W to 0.25W, which would be audible in terms of loudness but perhaps mire importantly, produce clipping ('crunch') and not affect lower output levels (audible as 'compression' or

).
Cheers. Thanks again. This has my brain working hard - always a good, fun experience.