I rectified the issue today by swapping out my 16GB GS4 for a 32GB GS4. I went from the legendary 9.62GB remaining storage to 23.04GB remaining storage, and my wallet is $88 and some change lighter for the effort (with tax). But I'm happy with AT&T for working with me to do the swap since I was sorta-kinda outside the 14 day window.
I checked a display GN2 while there (also a 16GB device) and found that it had 10.9x GB remaining storage. A little better, but not much.
Now on to the task of setting my GS4 back up like the old one... or as close as I can remember.
Edit: while I was there swapping out my 16GB unit, the Samsung rep was in the store and I chatted with her for a while. She was very aware of the issue.
Surprisingly, the store personnel said they have not had much pushback from the customers on the issue. Yet.