Do you know for sure whether it's a 360/ other? Find out which engine, look at the driver's side front of the block immediately below the deck. Should be a long string of no's. Your CID will be I thing no's 2, 3, 4, as in X360XXX...... I believe.
Then crawl underneath, remove the front cover on the trans, and see if the torque converter has weights on, or if it has a stock/ non stock flex plate
Have you determined if it's ENGINE vibration, or IN MOTION? That would be the no1 job.
If you determine it's "engine" remove the belts and see if that changes things. I used to fight an aftermarket A/C setup until I found that the belt was harmonically vibrating, all it took was to turn the idler on it's pivot, and substute a different belt length.
Next would be to eliminate tires, and check rear wheel bearings for play. If possible, swap another pair of tires on the rear, or even rotate the tires front/ rear.
Check U joints, REMOVE THE SHAFT. You cannot check U joints with shaft in place, as they can rust/ become dry and "seem tight."
Check pinion for slop--might be leaking-- and check pinion angle
Inspect drive shaft for obvious missing weights (mysterious patters/ rust spots) and dents or other damage.
