I figured it out... I did some more digging and read the config-dist.php file in Moodle. I ended up registering our IP with a no-ip.com. That worked! Now I can at least further test things out of the district. Then I'll get things set up properly with our own FQDN.
Thanks folks for making me think more! Sometimes that's all it takes.
For those reading this thread for an answer... You need a FQDN in order to use Moodle outside of your LAN. Use a free service like No-IP.com to do this and it will work.
Read this for more info...
https://docs.moodle.org/34/en/Configuration_file#Setting_.24CFG-.3Ewwwroot_correctly