hi finn,
i agree with jim, check the entire drive line and closely inspect the two bolts that mount the center support bearing to the underside of the car. it sounds to me like you have some sort of a driveline issue, not necessarily a differential going out. if the driveline looks good ie. center support bearing, flex disc, u- joints, bolts etc. i would then drain the diff. and inspect for metal in the gear oil. also check the supporting tube slip joint mount. if you search rear axle differential mount replacement you will see it as part #151 in the illustration. mine went out some time ago and it was the cause of a clunk noise in the rear of my car. my "clunk" noise was only when i put it in drive or reverse, it wasn't continuous like yours but i assume if it was completely shot it could be. keep us updated, good luck.
bo
65 230 sl