I could see the thud being caused by the upper arms if they were loose enough to allow the top of the axle to move back and forth, causing the thudding. In that case the lower arms would be the pivot point. Whether that's the cause of your noise, it's hard to say.
Here's a diagram of the rear axle, to give you a clearer idea of how things are set up, in case it helps. They refer to the arms as links.
If you decide to tackle it, check out
my writeup on how to do it. If the upper arms are in need of replacing, I'd replace the lower ones as well. The good news is by doing this, you won't have to worry about the infamous death sway
