After a long time, I tried working on the gunner's wrist problem once more. I bothered downloading The Mancandy FAQ only to find out it didn't explain how the rigging in the wrist worked.
I tried searching in BlenderArtists and found a solution in a thread. It was this blend file in particular (made by doncuan) that gave me the idea. However, I did realize that I had modeled my character's mesh without giving forethought to wrist rotation. This other blend file (made by Vertex Pusher) demonstrates a much better forearm mesh designed to twist properly. I'll study it in detail when I make a new character.
I also modeled and rigged the gunner's weapon. Its not textured yet. After looking at it, I decided it looked too much like a fireman's hose, so I'm going to make a different model.