I’ve had more back and forth with the developers of Nextgen, who believe that the conflict is with how iThemes Security writes the portion of the htaccess file that redirects the login URL.
Specifically, they said they didn’t understand why it was written this way, and how line 2 below wouldn’t cause conflicts with other plugins.
Here are the lines they said were causing the conflict. I’ve edited out the private details…
RewriteCond %{SCRIPT_FILENAME} !^(.*)admin-ajax\.php
RewriteCond %{HTTP_REFERER} !^(.*)url.com/wordpressdirectory/wp-admin
RewriteCond %{HTTP_REFERER} !^(.*)url.com/wordpressdirectory/wp-login\.php
RewriteCond %{HTTP_REFERER} !^(.*)url.com/wordpressdirectory/location
RewriteCond %{HTTP_REFERER} !^(.*)url.com/wordpressdirectory/locationb
RewriteCond %{HTTP_REFERER} !^(.*)url.com/wordpressdirectory/locationc
RewriteCond %{QUERY_STRING} !^qmkjj0xqerhjkcygky4fi
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 /wordpressdirectory/not_found [R,L]