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.

Problem 1:

The sound is too bright (too much carrier frequency remaining in audio output)

Reason:

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.

Solution:

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.

Reason:

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).

Solution:

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.