I had a similar vibration (although only with the clutch partially disengaged)

Mine turned out to be the clutch. Not sure exactly which part of the clutch because I changed out the pressure plate, Clutch disk, throw out bearing, and pilot bearing.

 

That would kind of make since, maybe the clutch dish it’s self it off balance when unclamped from between the flywheel and pressure plate. Maybe it’s rocking back and forth perpendicular from the center ling of the transmission shaft? This is a center force clutch set up.

Bad u-joints is the most likely culprit followed by motor and/or tranny mounts.

Any time there is slack in the drivetrain it will behave differently on acceleration versus deceleration.

U-joints have 4k on them along with everything else in the drive train, either new or rebuilt from a total ground up restoration.

I ordered a new drive shaft yoke because it has wear on the outside and is causing the rear of my 4-speed to leak. The drive train feels very tight when goosing the gas.
I will also add that I had this same type of vibration all the time and I pulled the drive shaft and had it re-balanced and it mostly went away. The direction I’m going to go with it is pull the drive shaft and install a new yoke and have it balanced for a third time. Would it be worthwhile to have the u-joints replaced again?

 

Bad u-joints is the most likely culprit followed by motor and/or tranny mounts.

Any time there is slack in the drivetrain it will behave differently on acceleration versus deceleration.

 

yea definatly check the u-joints even if they feel tight they can cause a vibration, i have been down that road before and it turned out to be u-joints(after swapping alot of stuff out)

 

One other thing, is I recently bent the rear springs on the back of my car from wheel hop. Would that be a reason to replace the u-joints? I never noticed any drive line vibration after the bent spring incident. But this is the first time I recall running the car up that fast and pushing in the clutch. If I hadn’t pushed the clutch in to let the motor rev down I’m not sure I would have noticed anything.

 

Could be related, did you see any evidence of axle wind up? I've seen axle wind up enough that the rear of the driveshaft, front of the rear hitting the floor. Can ruin u-joints and or bend the drive shaft.

 

Mine had this problem, the way I cured it was I replaced my leaf springs and bushings. I couldnt believe the tremendous improvement after I did that. My leaf springs were original, they started vibrating around 60 or so MPH. Drives like a dream now.