Pushing the clutch to have the sound goes away makes sense to me, something is only unhappy under load. U-joints in trucks often do this.
The center bearing/bushing going bad may cause a vibration, but shouldn't cause a clunking. Mine was completely GONE, the bearing was almost seized and was spinning the rubber with no clunking.

Check the u-joint in the center and the flex discs for cracking and play. If a flex disc comes apart on you while driving, you'll likely destroy your driveshaft, check that immediately.

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1984 300TD -- summer daily driver
Many others that aren't Mercedes...