Thanks Q - I took it out to see if I could feel the vibration, and I couldn't.
And then as I was driving the same road as last night, the sound started at about 45mph, then started getting louder, and then I moved the rear part of the console around, and it stopped for a bit, then started back up but much more quiet than before (And at another point when I moved the console area around some more it stopped again). Even when it did start back up, even at 65 mph, the sound wasn't very noticable anymore.