Vibrating during acceleration

Car: 1993 Chevy C 1500 (2WD) manual transmission
Background: The car sat unused in a garage for 2 weeks (no problems before this) the first drive after its break, the pickup almost felt like it was slipping and power was not getting to the wheels. The vibrating began the next day. The vibrating is very obvious and unpleasant under acceleration at approximately 2000 RPMs in any gear. Grease was injected via grease zerk into the center carrier bearing area and the vibrating was marginally better. Today the back end of the truck was lifted up and put into gear and brought up to 30 MPH. The pickup was then lowered and a test drive revealed that the vibrating was considerably diminished.

An inspection of the drive shaft reveals:
no vibrating in neutral
the U-joints are not loose or leaking;
the drive shaft has 2 small dents which are countered on the opposite side by weights;
the drive shaft will move up and down ~1 inch or less if pushed in bench press fashion near the carrier bearing;
the drive shaft does not move in the direction of the length of the vehicle;
the driveshaft will rotate freely 1/16th to 1/8th of a turn before it is stopped by the back of the transmission or the rear differential;
no mud clods in wheel wells;
new tires properly inflated

Questions:
Is the slight rotating and movement of the driveshaft normal?
why would the vibrating have diminished if I spun the wheels?

any ideas will be greatly appreciated

Thank you

I think that you have a bad U-joint about to fall apart.

when you raised it and ran it without a load the joint centered itself. And when you took it for a drive it just happened to stay that way. Soon it will become out of center and you will get the vibration back…or the U-joint will fall apart on the road and could do damage.

It sounds like you will do this yourself, so I’d just replace all the u-joints and the carrier bearing.
Cheaper to take it all apart only once.

Be sure you mark both yokes before removing the old joints and realign the marks when assembling it, or it will be out of balance and you’ll get a new vibration and think it’s the old one.
A good bench vise is normally enough to press the new bearing cups in.

Yosemite

To check for worn U-joints, raise the rear of the truck so both rear tires are off the ground and place the transmission into neutral.

Now rotate either of the rear tires back and forth while observing the U-joints.

If there’s slop in a U-joint, it’ll be pretty evident.

Tester

Replaced front and rear U-joints and inspected middle u-joint and found no problems. Vibrating still occurs. Any other Ideas?

Replace the carrier bearing.

If you can move the shaft up and down almost an inch next to the carrier bearing, as you describe, you have a bad carrier beating.

There is a black rubber cushion type ring around the carrier bearing. A detailed picture found here. The whole assembly is bolted down tight but the rubber and the bearing together can slide up and down in the metal housing. I checked for the same movement on another car and it moved also (not quite as much) so I figured that movement was normal.
Any second opinions?

When I started reading, my first reaction was the carrier bearing. Then I saw the business about the grease and all the other things done that also seem to point to the carrier bearing.

Yup, that is likely it!

The problem was a single shorted out spark plug wire. I could not see the wire shorting out because the exhaust manifold was in the way.
The shaking completely went away after I wrapped the shorted portion of the wire in some electrical tape.

Great! but regard that fix with electrical tape a temporary solution, and get a new wire (or replace all of the wires if they look to be in marginal condition).

I’d also put some heat shrink tubing on the wire where it abrades against the manifold. Or be sure to route it so it can’t contact the manifold.