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I agree with Mike about the clutch/pilot bushing wear and the post about the clutch/pressure plate balance. The only way to really find out is to take it apart and see if you can spot the problem then reassemble with everything in spec.
I want to add my experience FWIW about a issue we had on a truck transmission years ago that took me a while to figure out. In the end the input gear had wore where the mainshaft pilot slides into it and the roller bearing inside started to come apart. My memory tells me the mainshaft was fine but the input gear had to be replaced with a new roller bearing and made a huge difference..
Point is everything had to come apart to find the problem.
Harmonic balancer tight? Outer ring not moving around? Check with a timing light.
My buddy Bill just had the same symptoms of a vibration on his 67. His balancer spun and actually fell off the hub. He was having slight vibration at neutral more pronounced at speed.