UPDATE
Okay, folks. You deserve an update. I have found the source of my sound and It has been corrected.
First of all, the sound is coming from the
front of the car, not the rear. I discovered this after I lifted the car up, checked the tires and lugs, then started the car, put it in gear, and watched the wheels and axles turn. There was no noise, no clunk, no anything. I checked for axles wobbling, etc. I checked at different wheel speeds. I couldn't find anything wrong.
Then I decided I'd check the front of the car and I discovered two missing lug nuts from the passenger wheel.
Holy crap. Two other lug nuts were loose! This freaked me out more than if an axle was on it's way out. I have no idea even when I last had that wheel off, so I'm curious as to what happened (all the other lugs were tight).
I waited until today when I could get some spare lug nuts to see if the noise went away, and sure enough it did. I seem to have caught the problem very quickly because the studs were fine and the paint on the wheels wasn't even scratched, let alone the bolt holes being out of round from moving around on the studs.
TL;DR: I'm an idiot. The noise was coming from the front and it was two missing lug nuts that was causing my issue!!