Solved the mystery of the redirect on exit. There were some extra lines of code in the .htaccess file that somehow were not removed during the plug-in deletion & updates.
Took all this out and it all works beautifully. <secret code string> is the long list of numbers/letters were created in an early version of Better WP Security when choosing to hide the backend.
RewriteRule ^login/?$ /wp-login.php?<secret code string> [R,L]
RewriteCond %{HTTP_COOKIE} !^.*wordpress_logged_in_.*$
RewriteRule ^admin/?$ /wp-login.php? <secret code string>&redirect_to=/wp-admin/ [R,L]
RewriteRule ^admin/?$ /wp-admin/?<secret code string> [R,L]
RewriteRule ^register/?$ /wp-login.php?<secret code string> &action=register [R,L]
RewriteCond %{SCRIPT_FILENAME} !^(.*)admin-ajax\.php
RewriteCond %{HTTP_REFERER} !^(.*)com.au/wp-admin
RewriteCond %{HTTP_REFERER} !^(.*)com.au/wp-login\.php
RewriteCond %{HTTP_REFERER} !^(.*)com.au/login
RewriteCond %{HTTP_REFERER} !^(.*)com.au/admin
RewriteCond %{HTTP_REFERER} !^(.*)com.au/register
RewriteCond %{QUERY_STRING} !^ <secret code string>
RewriteCond %{QUERY_STRING} !^action=logout
RewriteCond %{QUERY_STRING} !^action=rp
RewriteCond %{QUERY_STRING} !^action=register
RewriteCond %{QUERY_STRING} !^action=postpass
RewriteCond %{HTTP_COOKIE} !^.*wordpress_logged_in_.*$
RewriteRule ^.*wp-admin/?|^.*wp-login\.php /not_found [R,L]
RewriteCond %{QUERY_STRING} ^loggedout=true
RewriteRule ^.*$ /wp-login.php? <secret code string> [R,L