Wow, @jfb, thanks for the speedy reply! I tried that and it didn't work.
However, I actually just figured it out. Based on Pihole resolving its ip as internal IP - #2 by Bucking_Horn - the issue I was having was defining domainname and hostname in my docker-compose file. When I removed those, I was able to reach the admin panel via https://pihole.[server-name].lan