Bad motor mounts cause the car to clunk when your dirve it.....

I would look at the other parts of the drive shaft including mounts, bearings. Have you looked at your differential?

Hi Brewtoo,
I had a really bad vibration on my '75 280 that was most noticeable around 35mph, and it turned out to be the plastic bushing that the driveshaft front centering pin goes into, and that keeps the driveshaft centered - it was worn out and didn't keep the driveshaft aligned. Replacing it wasn't too hard, and it was very cheap to buy. (The driveshaft sort of "plugs" into the rear of the transmission as it fits up to the flex disk, and the plastic bushing is what holds the shaft centered - the one on my '75 was goose-egged from wear)

If it weren't for bad luck...
 

Yesterday, I did this entire job over again. This time, rather than leave the driveshaft in and replace the flex disks front and rear, I removed it entirely and replaced the center bearing and carrier. BTW, all of this is not a hard job but it is intimidating if you've not done it before. It does take some time.

Anyway, I removed the old bearing and carrier (which looked and felt fine). I did the trick of heating up the new bearing to about 200' and plop! it fell right into place on the shaft.

People say that the big 43mm nut is usually not very tight. Mine was tight. I had to hit the wrench with a hammer to get it loose.

I also replaced the trans mount, which had sagged a bit.

I put it all back together and drove it. No vibration! Until......

This morning the temp was in the 50s. I got in the car and headed down the street and Dang! the vibration was back starting @ 35mph.

It is temperature related and load related. Cool temps and no/low load is when it vibrates.

I notice that the trans mount crossmember has slotted holes so that it can be adjusted from side to side. It sits all the way to one side. Evidently came from the factory that way. I wonder if it should be more centered?

The driveshaft sections came with the factory alignment marks. However, they were not lined up exactly...probably 15 degrees off. I think it came this way from the factory. I doubt 15 degrees would make a big difference. I put it back together the way it had been for the last 16 years.

And the u-joint. Should I feel any detent in it? It has a mild detent in both directions that will stop it and hold it exactly straight. Is that normal?

And the centering sleeves have no noticeable play.

Hi Brewtoo,

That U-joint should be perfectly smooth, ie NO detents... the detents most likely mean that there's a little wear that's causing the "notching" effect. I think you better plan on replacing the U-joint.

Yes...the u-joint has roller bearings and a cross shaft.. x/y movement should be perfectly smooth. When there is notching, one of the rollers has worn a slot/notch into the cross surface and the notching you feel is the rollers popping in/out of the wear notch..probably more than one.
Time for a joint ..:)
Get one with the greazzzze fitting if you can find it.