Well, it sucks, but I had to give up on this project. I now have a better understanding of how these things should be wired, but in this case it was a bit too risky for me to play around.
I cannot see any wire nuts inside the box, but I'm pretty sure they're probably located somewhere in the walls. If the wire setup was a bit more standardized, I might have been able to figure it out. Oh well!
I went ahead and purchased one of those remote light switches. I installed it right where the old one used to be (after putting a wire nut on each of the old cables), and it's working like a charm now. Thanks for all your help and for sticking through this whole thing....it's a shame we couldn't figure this one out.
I pulled the tab to see what would happen, and the switch sort of worked. The bottom plug became an "always hot" outlet, and the top plug turned on and off with the switch. The problem is, now the next three plugs in the run also turn on and off at the switch. I assume this can easily be fixed by adjusting one or two of the wires. Any ideas as to which ones?
Swap the black wire from the top to the bottom of the outlet and the bottom black wire to the top.