Hey all! I figured this out. The problem had absolutely nothing to do with the Mastodon Docker container!
The issue was that I use Webmin to manage a lot of my Linux server and the server itself runs Apache web server. When I had created a subdomain for this Mastodon instance to live via Webmin, Webmin automatically created a few re-directs in my global Apache configuration file for /.well-known addresses to the domain.
I commented out those redirects and voila! My Mastodon instance federates as-expected.