I have made zero progress this week, as the entire thing was spent failing to figure out this problem never mind resolve it.
Basically what's happened is that every time I go to bake (and it doesn't seem to matter what baking option I choose, there seems to be a few), the sculpt mesh decides to do this at some point either just before the bake starts or right at the beginning somewhere:
Which results in a very messy bake:
I struggled with it for a week before finally giving up and asking the forum for help (and feeling bad about going there for help after 3 years, don't ask I don't know either).
Hopefully someone will be able to point me in the right direction if the problem ever crops up again. In the meantime in the interests of getting this character done I'm just going to paint the normal map.
This work by bek (ryivhnn) is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.