I had the "thump/rattle" that I have read many E55 owners have in their rear deck area with the sun shade option.
Under the deck in the trunk, there are three threaded studs coming out of holes practically hidden in the sheet metal deck. On my car, the nut on the stud to the far left was missing.
I replaced the missing nut, tightened the (loose) other two, and my "Thump" is gone. I am Thumpless and loving it!