bad vibration

I am trying to find a vibration that came on suddenly. I have looked at tires for cupping and replaced 1 steer. I don't find an obviously bad u-joint, motor mounts look good, ride height is ok, no loose wheels, flywheel housing bolts are tight. I have thrown the transmission into neutral and the vibration stays the same. I haven't looked for missing weights on the driveshaft or drums. The vibration starts at 30 to 35 mph and is severe at that speed but it doesn't feel any faster or worse at higher speeds. A while back I put on 8 drive tires. I had to replace 2 because of odd ball cupping. One more now shows that same cupping. Maybe replace the remaining 6. I hate to just throw money at it. Any thoughts?

 

Update. No parts or pieces layer in the flywheel housing. No broken springs in there. Last night with a laser temp. gun I hit the u-joints and wheel hubs. One u-joint had one cap that was 30 degrees higher than all the others. This morning I found one u-joint cap that has turned less than one full turn under the strap. I will be checking that out. (Two different u-joints). All the wheel ends had similar temps.
I don't see any loose fasteners or beat out bushings.
The vibration is about the same loaded, empty or bobtail.

All steering components are tight.

Shocks are at 300,000 miles.

The shake comes on hard and all at once at 30-35 mph. It is as hard at 60 as 30. I'm not sure but when I let off the accelerator it seems to get worse for a few seconds. No hum. No noise. Just an intense vibration.

I thought about an injector but I don't have anything leading me in that direction.

I have some centering pins but not on this truck. The fronts are Budd wheels. Rears are hub piloted.

Once the vibration starts at 30-35 mph, it seems to remain about the same in all gears, all rpms, and all speeds. I know that makes no sense.

 

No tire work or mechanical work has been done recently.

 

I am the only driver. I always make sure that the wheels are not turning before engaging the diff. lock. Foot on brake pedal on hold for a couple of seconds.
@bjrc I didn't know that about the bent thru shaft. Thanks.