It was only after researching later that I discovered that this wasn't currently possible and recommended approach was to buy some replacement internals that cost more than the device itself (and if I recall correctly, more than the new Home Assistant Voice Preview Edition).
The hardware in those devices is generally better, most of them have much better speakers, but they're locked down, the wake-word detection hardware isn't open or accessible so changing it to do what we need would be difficult, and you're just hoping there's a way in.
Existing examples of opening them (as in freedom) replace the PCB entirely, which puts you back to square one of needing open hardware.
This feels like the right approach to me; I've been building my own devices for this purpose with off-the-shelf parts, and designing enclosures, but this is much sleeker; I just hope an add-on or future version comes with much better audio out (speakers) because that's where it and things like it (e.g. the S3-Box-3) are really lacking.