I only tested long enough to hit the error once, which didn't occur during multiple navigations of the site until I attempted to login.
When the issue occurred, what I notice in the URL the browser is being directed to is that it's trying to force port 80:
So I suspect that's the issue; this URL is trying to force HTTPS use, but over port 80 (where TLS/SSL isn't enabled) instead of 443 (the default for HTTPS URLs, and where TLS/SSL is enabled on your site).
In ACP, General, Server Settings is the "Force server URL settings" enabled? And if so, is it set to force port 80? Try changing that to 443.
If "Force server URL settings" is not enabled, maybe one of the redirects in .htaccess is attempting to append :80 to the rewritten URL?