Well, managed to fix the logout issue.
However, since Windows is the gift that keeps on giving, another thing is not working (well, it has been for a while, but I never bothered to ask about it until now) is mapping WebDAV servers using the 'Map network drive' feature:
Meanwhile, on every other modern operating system ever, it works. And now that I have my own WebDAV fileserver, this is a rather big issue.
Once that is fixed, this machine will work perfectly*.
*Until Windows fucks something up again, which it will, eventually.