Perhaps you have me headed in a new direction. But so far, no go. Changed my tunnel to use port 443 instead of 80. As shown below I get the same results.
I enter: http://127.0.0.1:8888/phpmyadmin/
URL changes to: https://argfam.net/phpmyadmin/
And I get message: "For security reasons, this URL is only accessible using localhost (127.0.0.1) as the hostname."
The solution I had found to redirect all incoming traffic to always use SSL was to modify the bitnami.conf file as shown below. This file is located at: /opt/bitnami/apache2/conf/bitnami
Redirect permanent / https://argfam.net/
That seems to work fine other than I can no longer access phpmyAdmin after creating the secure tunnel using PuTTy and trying to navigate to http://127.0.0.1:8888/phpmyadmin/ (which worked until I did the port 80 redirect). So now thinking the redirect approach maybe is the culprit. What I did to get access was to change the bitnami.conf back to not redirect port 80. Still had some issues as it seemed that the redirect was cached or something. Kept going to ssl even after restarting Apache, then all the bitnami serfvices and even stopping and starting my Lightsail instance. Eventually it did not redirect and was able to get to pypmyadmin as needed. Not sure how to flush that redirect.
Will see if there is maybe a better way to redirect as thinking that might be the issue.