Also, as another status update, I'm pretty sure that the hot GPU was defective because it shorted. Sparks were flying and everything. I'm honestly surprised (and fortunate) that nothing caught on fire. I've told Gigabytes and will hopefully get a refund.
One of my gigabyte 7970s started sparking too! Scary business. There's no ozone smell of a good arc, but it's a pretty big burst of sparks coming out of the top heat sink.