High speed vibration

I just bought this 89 GT. Nice car but has a few bugs. one that Im dealing with now is a vibration to the rear of the driver. I ve owned several Mustangs but never ran into this before. At 65 mph I develop a vibration which appeared to be connected to the driveline. Put it on the lift and shook the driveshaft thinking the universals are bad. Not so. Universals are tight, but There is a little shaking where the driveshaft goes into the rear of the trans. There is also a little turning (think the mech called it lashing?) of the shaft at the rear end. I consulted a driveline guy who suggested balancing the shaft.$125. If its not that it could be the bushing at the rear of the trans. $125. If not that some type of thingy in the rear end. $200- $500. What do you guys think? anyone run across this before?

1st of all, thanks for the response and I will chk for the weight as soon as I can get the car on my lift..... but is the drive shaft supposed to have play in it when you turn it back and forth. It has about a 1/2 to a 1" play. If it isnt supposed to have play would that cause it to vibrate, and whats the fix?

Thanks for your imput. I have no idea what gears it has, however, it turns2000rpm s at 65 mph. It is a 5 speed. Is there some way to determine the gears without removing the diff cover. Oh, by the way, I just ordered an aluminum drive shaft from LMR, along with a safety loop and new bolts. Hope that does it! If not I ll look else where I guess. Any other suggestions? The driveshaft remains suspect.