Got it working. A couple of things:
I had to change the configuration of the network so that the Airport was at the top of the list (which it already was), followed by the built-in ethernet (even though no other ports were active).
You can not test the connection from any computer inside of the Airport network. It fails every time. I had to take one computer and connect it to a dial-up connection to test it. Worked fine every time.
I DID have to forward port 548 specifically to the machine in question to get it working, otherwise it would fail.
The only sharing I have turned on right now is Personal File Sharing and Printer Sharing. The firewall is active.
Since I'm set up thru ADSL with a dynamic IP address, I signed up at
www.no-ip.com to get a free address and downloaded their free OS X software to keep their servers notified whenever my external IP address is changed. This way I don't have to worry about chasing around the IP address myself.
This will do what I was hoping for. However, what are the security concerns with mapping port 548 directly to my machine? Is there a better way for me to accomplish the same thing without loosing security?