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You need to recheck your tranny. Just because you put it in neutral doesnt mean the output shaft quit turning...lol. Generaly speaking if you have a vibration in the " float range" where your not accelerating or decelerating its in the drive shaft or some part of that assembly. It could be pinoin,yoke,slip tube,u joint...66 has the 8" rearend correct? Could be the rear support bearing for the pinoin.
If you bought a new drive shaft for this car make sure its not too short or too long for that matter. Too short will cause a hell of a vibration...too long is really hard on parts.
just thinking outloud.
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" If it wont break em loose in 3rd gear, it aint enough power "
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