Wow, thanks for all the help, especially from the not-so Lazy_Perfectionist.
I also called tech support (several times) and got essentially the same advice as LP's. I have tried both port forwarding and port triggers to no avail. Although, when I try port forwarding I get a message that indicates that I also have to open said port in my firewall (but doesn't indicate how this would be done).
I think despite all the helpful advice I have received, and the many hours that I have put into the problem, I am going to have to punt. I think I will run both the mac firewall, and the modem firewall, and just toggle off the modem firewall when I am uploading/downloading turns. Not exactly convenient. But it is secure and I can stop pounding my head against the wall trying to come up with something more elegant.