Can rename login page be used over HTTPS?

I have been evaluating requiring SSL on one of my WP sites, including one for which I am using the AIOWPS Rename Login Page brute force prevention feature. In my development environment, if I use a Redirect statement or mod_rewrite rule to force http to https, I find I can no longer access the renamed login page. For the Rename Login Page settings, it looks like the login URL is hard-coded to http://www.sitename.com/ so whatever slug is chosen gets saved as part of a http URL. Is there any way to update this so the full secret login URL (with the slug) is HTTPS?

https://ww.wp.xz.cn/plugins/all-in-one-wp-security-and-firewall/