340 Engine Shake

I went through a similar issue years ago, and it ended up being an out of balance pressure plate. I had always assumed the pressure plate threw a weight, or wasn't properly balanced from the factory. I installed a new one and issue was gone, but yes I had a bad vibration at idle in neutral or driving in gear, the dash would rattle if I revved it at idle that's how bad it was. I got good at pulling that 4 speed in less than an hour because I was trouble shooting it every night after work, I had the flywheel on a balancer, then replaced throwout bearing, etc. It was a PITA figuring it out.