Found the solution.
Under the Login Plugin config you need to set the “Dynamic Page Visibility” option to Enabled.
With all the other above settings, this works. Now the issue is caching leaving things visible even after log out and having to refresh a page to flush the page’s cache. Disabling caching addresses this but that seems a little extreme.
Documentation on the Security settings could be seriously clarified to avoid the need to sift through the unofficial documentation here.
Might also be nice to compile a separate set of documentation on how to accomplish things using the Admin interface instead of defaulting to modifying the code manually for those that are less confident in that area.