I replaced the engine mounts, shocks, axles and exhaust hangers within the last 5,000 miles. The exhaust system is patent: No holes. I replaced the differential fluid within the past year. Engine speed doesn't seem to have any effect on it: It happens when the car begins to move from a dead stop. I don't hear the noise when cruising at any speed. It almost sounds like something is rattling around in the trunk. It "rumbles" for about 3 seconds and then goes away. If I had to swear on it, I'd say I can feel a vibration as well. So very faint however.Definitely sounds like its coming from the trunk. My impression is that something is under more stress at the time of accelerating from a dead stop than at any other time and this is what's failing.
I'm by no means an expert mechanic but I have kept this baby together on my own for a long, long time.
Thanks for your input and thoughts.