Bob and others:
As promised, I wanted to get back to you all with the "solution" to the issue I have raised here. So let me first lay out what I have learned in the process...
1. Contrary to what was suggested, not having the Apple router support UPnP is not the stopping point. The Apple Airport Extreme does not support UPnP but offers an alternative called the NAT Port Mapping Protocol, which is an Internet Engineering Task Force Internet Draft. NAT-PMP allows a computer in a private network (behind a NAT router) to automatically configure the router to allow clients outside the private network to contact this computer. Therefore, while it is "technically" correct to say that the Airport Extreme doesn't support UPnP, in reality it allows the mapping to occur with NAT-PNP.
2. It appears the actual key to the solution had nothing to do with the ISP blocking ports (as our tech people claimed) but, rather, making sure that the Airport Utility window that allows for port mapping to occur is completed correctly. What is interesting is that the choice that can be made with regard to the "public" and "private" entries into this window. Some had suggested that the port number related to the static IP address assigned to one of my cameras should be in the "private" area of the window. But, as it turns out, this need not be the case. It all depends upon how the camera settings have been chosen. In my case, the HTTP port number is in the "private" section of the port mapping window and the unique port number assigned to the static IP address for the camera is in the "public" section.
3. As I mentioned earlier, I have Axis cameras installed. And I was told that part of this solution has to do with settings for the camera itself, in addition to using Airport Utility correctly as described above. Unfortunately, I did not catch the details on this from our tech people but just know that this appears to be the case.
If you will allow me just some personal commentary on this issue, here goes:
It occurs to me that a lot of people are beginning to become interested in remote access to various aspects of their homes. But, given the experience I have just had, it is also quite clear that the majority of people will not have the time, patience, or capability needed to wade through the myriad of technical issues that must be addressed in order for this to happen.
What seems likely is that larger players (and Apple certainly would be among them) will move toward an easier "plug-and-play" solution which would take most of the pain out of this process. I have heard that Apple TV may be the core element for this if Apple decides to move in this direction.
Finally, I want to express my appreciation for everyone who was willing to weigh in on this issue. Not every suggestion was relevant or useful but no one should expect this. Instead, everyone added pieces to what eventually turned out to be the solution. I am truly grateful for this.