The task becomes a lot easier under Apache. So I threw away the plugin code and added the following rule to the Apache configuration:

<directory "/public_html/mysite.com">
RewriteEngine on
RewriteCond %{HTTPS} !=on
RewriteRule ^(.*) https://%{HTTP_HOST}/$1	[R,L]
</directory>

The directive above can be placed inside a VirtualHost or Directory directives, but this usually requires access to the Apache server configuration, which is not typically possible in a shared hosting environment — in that case, the rule can be added to the .htaccess file.

Alternatively we could have used the SSLRequireSSL Apache (2.x) directive, but this would only block access to the non HTTPS address. In our case we want to automatically redirect the users instead of displaying an error message.