Be sure to check your config (app_local.php and app.php in the config folder). It looks like the fullBaseUrl attribute can be set to override the HTTP_HOST env variable that looks to be causing you trouble.
If that doesn’t work, you should be able to do this via your webserver. Here is a tutorial for NGINX and Apache.
Another, and probably the easiest option, is to just use CloudFlare. They offer an “HTTPS Rewrites” setting/option that will automagically rewrite all requests to HTTPS.