I ended up discovering the problem and thought I'd post it to help anyone else out. (In retrospect I should have stated that I was modeling in 3ds Max 6. I forgot
After I applied another Edit Mesh to the top of the stack I realized that I couldn't attach any new faces/polygons without messing with the UV maps that I had done.
Then I discovered that I can detach surfaces and they will correctly display their pre-assigned UV coordinates without any problems.
(I was able to make my model still work without having to do any remapping.
(I think I had misunderstood a line in Spacemonkey's JO model tutorial, because I looked at it again and understood what he was talking about with how he segmented his model.)
So, the mesh can be unwrapped with parts attached that will need to be mapped together to ease the texturing process , and then those parts can be detached by applying another Edit Mesh modifier to the top of the stack, selecting the surfaces, selecting detach and giving them the correct name for the JO/JA segmentation guidelines.
I hope that made sense and can help someone else with their problem. (Even though it may have just been a somewhat ridiculous oversight, but this is my first model period, so some trial and error was required.