Well, allow me to answer my own question for future generations. Turns out that you can indeed wrap the ThemeProvider with a StylesProvider with a generateClassName argument:
const generateClassName = createGenerateClassName({
productionPrefix: 'coreJss'
});
...
<StylesProvider generateClassName={generateClassName}>
<ThemeProvider theme={MyTheme}>
Stuff
</ThemeProvider>
</StylesProvider>
Now, your production classNames will be coreJss1, coreJss2...
for that package and jss1, jss2...
Now, you might ask 'why didn't yours work in the first place?' and I would tell you to pay close attention to what you actually committed vs. what you typed and didn't save.
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