If you have tried putting it into neutral while at speed and you are still getting the vibration here is a list of things that can cause it.
1: Bent, twisted, warped tranny output shaft.
1: Can be seen at the driveshaft where the shaft goes through the seal on the back of the trans. Look at the seal as you rotate the shaft (trans in Neutral) for the seal to get compressed more and less as the driveshaft is rotated.
2: Bent, twisted, warped slip yoke.
2: With the car in the air and trans in neutral place something close to the U-joint area where it curves into the machined section of the yoke (I use a 4 pound sledge hammer with the handle sticking up)and rotate the shaft. watch for the distance from the yoke to the hammer handle to be DIFFRENT in 180 degrees in several spots.
3: Foward U-Joint bad
3: Check with the "wiggle" test. Also pry between the yoke and the U-joint to check for thrust wear, It is rare but while your under there might as well be thorough.
4: Driveshaft warped, twisted, bent.
4: Same process as the Yoke test.
5: Driveshaft out of balance.
5: Cannot be checked at home but look for broken remnants of spot welds where balance weight USED to be. Also may be clean or less rusty
6: Rear U-joint bad.
6: Same as front
7: Loose, warped, bent, damaged pinion.
7: Look for sighs of impact damage from road debris. Pull on the drive shaft towards the trans and then towards the rear, looking for the rear pinion to move in and out. There should be NO MOVEMENT. If therer is then the pinion bearing is gone or on the way out. Check for runout with the "Hammer handle test"
8: Broken chipped teeth on the ring and or pinion gear.
8: Remove the rear cover and visually inspect.
9: Warped, bent axle. (Check at the same time as #8)
9: With the car up, wheels off, rear cover off. Look in the center of the carrier (thing with the big gear boloted to it) and you will see the end of the axles. Rotate axle until you see what look like a washer with one side missing(this is the "C-clip). Rotate axle until this gap is pointing to the front of the car. Push on the face of the axle where the wheel mounts towards the center of the car. Should move @ 1/4 inch. With a magnet and/or needle nose remove the C-clip. Slide the axle out of the rear housing. Tape around the splines that go into the carrier. Check for warp by rolling on a flat floor. A straight axle will just roll around, a warped or bent axle will have a "heavy" side and always stop with the warp towards the floor.
10: Wheels out of balance
10: Have professionally balanced
11: Wheel and or tire out of round.
11: With the car in the air use the "Hammer handle test" on all wheels
Sorry for the long post but with the car having been placed in neutral while at speed and the vibration not changing that eliminates the motor and "most" of the transmission. That only leaves the items listed above. I hope this helps and good luck. Jon Hanson