After some forensic investigation, I have identified (and, I think, solved) my two remaining issues with the V5 PCB, but I would be grateful for any feedback about my MIDI solution.
The sound is too bright (too much carrier frequency remaining in audio output)
This one was pretty dumb. I'm using the twin-T notch filter design from the Mozzi website but I made a mistake transcribing this circuit into my schematic, meaning that two of the capacitors have switched places.
I (clumsily) desoldered C3 and C7 and swapped them over. The audio output now sounds fine.
Connecting a MIDI input results in audible tones and clicks through the audio output.
Something to do with grounding or decoupling? It feels as though the MIDI input's optoisolator (a 6N138) is perhaps being a bit heavy-handed with its use of the available electricity (please don't disqualify me from the site for this appalling lack of understanding).
After lots of googling, I stumbled onto this seemingly similar problem and decided to whack a big (1000uF) capacitor across the 6N138's power and ground. I tried smaller values but to no avail. I suspect that adding a smaller (but still big-ish) capacitor to the LM386 and also maybe the ATmega328 might be a better solution, but I've already made a mess of the PCB! For now, the noise is virtually gone, so I'm calling that a win.