You could try some single-purpose plugins similar to this one
https://ww.wp.xz.cn/plugins/ws-force-login-page/
(I have never used this particular plugin)
in addition to the plugin you already have.
Test to see if there are any conflicts before installing it in a production environment if you choose to go that route.
Use https://ww.wp.xz.cn/plugins/members/ to make your site visible only to logged in users.
@carike do the people looking at my website have to have a wordpress account?
No.
If you are hosted on WordPress.com (or possibly with a Jetpack integration), they have the option to log in using their WordPress.com account, but on a self-hosted ww.wp.xz.cn installation, the only party they have an account with is you.
Their information is stored in the wp_users and wp_usermeta tables in your mySQL database.
