Finally! At long last (a few days), I have finally confirmed that IRC is working correctly on my server!
Basically, I gave tech support a call and they set up my server to be in the DMZ. I’d already tried this a few times, but every time I configured the server to be in the DMZ, the router would say that the device was off. This time, however, I just rebooted the server so that the router would recognize that it was online, and after that everything just started to work exactly how I wanted it to. It was glorious!
Finally, I can set up my SSH and my IRC servers to be on non-standard ports and confirm that they are working exactly the say that they’re supposed to. And I don’t think that the server is less secure by all that much than it was previously.
This is all too cool! I now need to take some time to learn how iptables works so that I can have that extra bit of security if I need it.