I think I may have come across the source of my rattle.
Follow the link to this diagram: http://parts.nalleygmc.com/images/pa...09GM07-044.JPG
Item 49 on the diagram seems to be the source of the rattle. If I put a screwdriver on the center part of this isolator while someone is kicking the tire I can minimize the rattle. The only problem I have is, what on earth is this thing called? I think these are the GM part numbers for this item.
15237959 INSULATOR. Rear Axle Control Arm
15237958 INSULATOR. Rear Axle Control Arm
I'm going to try and go to the junk yard tomorrow and see if I can take one off to figure out the mechanics of how it is mounted and to see how hard it is to remove the mounting bolts. If the one I take off looks in good shape, maybe I'll use it instead of trying to order a new one. I don't believe I'll be able to source this part from one of the local parts stores.