Check your motor mounts/bushings for a broken mount or a cracked bushing.  The engine can move enough to cause the exhaust to touch and vibrate.  Sometimes it will actually sit back in place properly, and everything seems ok, but the engine torques over on start up and can cause your vibration.  Just a thought.  Joe-JDC

JDC

Not sure but dual exhaust at least on my '55 routes through openings in the frame.  I get a vibration/rattle on occasion, usually when backing up in my case, which I attribute to the exhaust knocking against the frame opening.   It's near the front seat, if I remember correctly.  Maybe if you have dual exhaust passing through the frame on your '56 you should grab it and shake it to see if it rattles against the frame.

Again, this is just an idea.  I could be all wrong.  And often am!!

My Car has developed a Vibration / Noise in the last 2 Weeks. Its a light Vibration with a "drumming" Noise that repeats louder/ lighter. The Vibration is through the Floor not Steering. I have checked Brakes for Drag and Tires for Separation ( Radials). I pulled the Driveshaft Today to make sure new U-Joints were not tight and rotate freely and balance Weights are in Place. Motor / Transmission  Mounts are new and Tight.  The Vibration/Noise is diminished if I shift to Neutral . The only change I made recently was new Standard Mufflers and some Pipe bending. Nothing is touching the Frame. Any Suggestions?