Pontiac Montana 2006 sv6 with thump in rear end/suspension

I posted this problem 2 years ago and have attempted to follow some welcome suggestions. We still have the thump.
150,000 miles on this van.
After driving 15 miles on a maintained dirt road, I heard a loud, low pitched, (a low “B”) thumping sound. I couldn’t see anything loose.

The thumping occurs when we go over a bump, like a pothole, or between 65 and 70 mph. I’ve had a number of confident mechanics look at it, twice with electronic ears. I’ve been told that I should replace the rear end, that new tires would resolve it, that it was under the gas tank. No one has been able to isolate the thumping. Several refuse to take money for their time.

I have yet to replace the rear end. The RE is not very complicated since the car is front wheel drive.
New tires made a big difference; one of the old ones was separating.
Once, during service, they increased the pressure in the tires. The thumping got worse. I took it back and they decreased pressure. Thumping decreased.
For a long drive we attatched a loaded cargo hitch to the back. We hardly noticed the thump while the loaded cargo carrier was in place.
Strips of rubber inner-tubes placed under the straps holding the gas tank in place made the thump decrease, but not go away.
One mechanic lowered the gas tank, while I watched. He could not find anything loose or any signs of the thumping.

For bumps, it is only when the driver’s side rear wheel goes over a bump. I took the chairs out of the back, pulled up the carpet, and laid my ear against the floor board to see if I could pin point it. It seems to be in front of the rear wheel, about even with the back of the door frame, 14 to 16 inches into the car. It does not seem to be a vibration against the floor of the vehicle, but may be something hitting the fuel tank.

@bobert10‌

Worn sway bar links often make thumping noises

Bad shocks and struts, as well as strut mounts, can also make noises

I’m with db4690. At this age I am going to guess it is the rear shock (or strut if it has rear struts) and perhaps the mount. At 155,000 my minivan started thumping over bumps. I put in new struts and shocks and it now rides like a new van and is completely quiet over bumps.