Replace "You don't have access to this space. Go home" with prompt to login to access private space

Is it possible to replace the prompt on private Confluence Spaces so that anonymous visitors receive a more helpful prompt, such as "This space is not public. Login to access."

Our users are confused when navigating to our private wiki. For example, we send them to the homepage of our private wiki: https://biodiversitylibrary.atlassian.net/wiki/spaces/BHL/overview   The current prompt states: "You don't have access to this space. Go home". Our users click Go Home, which takes them to a list of only our Public Spaces, not the private space they intend to access.

If we direct them to our Confluence homepage, https://biodiversitylibrary.atlassian.net/wiki/spaces, they only see the list of public spaces, not the private space they are looking for.

The current login icon in the upper right corner is not obvious. If our users don't realize they haven't logged in, they reach out to administrators assuming they don't have the permissions to access the private space.       

I have reviewed various settings in hopes of making the user experience better for logging into Confluence to access our private wiki, but I don't see any obvious solution. 

We do not want to direct users to the main Atlassian sign on page as it includes other services (Jira) that we are NOT using and further confuse our users trying to access the private Confluence space.