I had a similar vibration in my signature car. I had three different driveshafts in the car, it was still the same. I suspected it was one of the axle joints, as the vibration was lessened with weight in the car, which would make the axle joints run just about straight.

I recently had the axles rebooted by CVJ, and installed them left to right to wear the other side of the joint. Vibration is gone, and is felt slightly on deceleration. These are the original axles, not replacements.

Keep in mind that a three-lobed axle joint combined with a 3.07 axle ratio will give just about the same vibration frequency as an out of balance driveshaft. If you really want to do some research, switch them side to side, and while they're out of the vehicle, run it in gear to check for vibrations, you'll only be running the DS and the ring and pinion. You can do it with the differential cover removed, the gears don't require any lube with no load, and you'll only be doing it for less than a minute.

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'83 300D, 126K miles.