I tried a couple of other things:
different cable: no difference
different gaming console: no difference
different monitor (Sharp LC20B6U-S LCD display): no difference. wait, what?
I'm seeing this shadow with entirely different devices, even an LCD monitor. Is this just a normal artifact of analog video signals? Do I need some special type of cable? It's true I can get it to go away with some games, certain color combinations and shapes. But generally, mostly, the ghosting effect is always there.
I have no idea what is going on at this point!