I wrote up a long "it ain't working" post, then had an "oh yeah" moment.
File ownership and file permissions. Make sure those are correct for your installation if that's something you have control over. Getting that wrong can apparently cause the redirect loop.
In my case:
chown -R account:account *
in the root of the installation did the trick. Your specific "account:account" will almost certainly vary.
Hope that helps someone.
Posted for documentation - no response required.