Classic/Antique Car Repair: Pulsating Vibration Noticable at most speeds, drive line components, wheels and tires

Question
I have a '58 Ford Custom 300 2dr. that has the original ford-o-matic with a '78 351w. Notice the pulsating vibration through-out the car starting at speeds as low as 20mph. Steering wheel, outside mirrors, etc. Car is stock except for the motor. Perhaps a flexplate? I've asked several technicians and they all give me the, "Well, it could be...." with no single tech saying check this first. Any help would be greatly appreciated.

Answer
When I am faced with this problem I usually start with a road test. I get the car up to speed and then shift the gear selector into neutral and let the car coast. If the vibration is still there the problem is from the back of the transmission to the ground and could be drive shaft, differential, or wheels and tires. If the vibration disappears the problem is transmission, flex plate, or engine and components. Also I would look for changes in the vibration with acceleration or deceleration. Wheels and tires will be constant while drive line components will most likely vary. I also turn the car right and left while the problem is happening. This loads the wheels on the outside of the turn and unloads the wheels on the inside of the turn. If the problem changes that could be a sign of a tire or wheel bearing. Once the road test has been done and the problem broadly identified then start checking components that the road test pointed to, but do not start tearing the car apart before narrowing the search down.
Brad