strategies to isolate cause of a "rhythmic" vibration issue

This is in an older Dodge B250 Van, with the Chrysler 318/5.2L v8 engine, not fuel injected.

On a recent long drive, I began to notice the van has what I can only describe as a "rhythmic" vibration issue whenever the accelerator is engaged. This is definitely new.

Basically, regardless of the speed/RPM, or amount of throttle applied, the entire van is shaking for about half a second every 3 or 4 seconds in a very repeatable steady rhythmic way. The vibration isn’t coming through the pedals or steering wheel, instead it’s the entire body of the vehicle where I notice it most, all the mirrors shake significantly, and the there is a low rumbling/vibration sound seemingly coming from all around.

At first I attributed it to the road surface, since the feeling is somewhat like driving on rumble strips at set intervals.

This vibration goes away immediately when I left off the gas, whether coasting at highway speeds (~100km/h) or lower side-road speeds (50-80km/h). Similarly, the moment I touch the gas, however lightly, the vibration comes back.

Braking appears unaffected, there’s no change in the braking performance at all and no vibration when braking.

I am trying to figure out how to narrow down the possible cause of this. It seems like it could be attributed to many things:

• Transmission, Torque Converter, or Flywheel?
• Wheels/Tires/Driveshaft?
• Ignition / spark plug / timing issue?
• Engine Mounts?
• Loose exhaust component?

To be clear, I’m not asking for details on troubleshooting all the stuff in this list, my point is that it seems like there’s a lot of potential causes for this, so I’m looking for some general early-stages things I might check/do to rule out whole categories and get into the right neighbourhood.