I had a similar problem with my Blazer.
Those are 42" Super Swamper TSL's. Six of them. All professionally mounted and balanced.
There are four shocks on the steering stabilizer.
Three shocks on each front wheel and two on each back wheel.
14 all together. And at times it could still shake your teeth out.
Every once in a while (more often than I like) the treads of all the wheels are in the nearly the same position (for lack of a better term, rotationally synchronized). No big deal in itself.
At a certain range of speeds (there was an upper limit that it stopped) which would vary by type of road, they would start to generate a harmonic resonance.
It would start as a hum, then vibrate, then start some serious shaking. It was setting off car alarms at the mall.
Sometimes, while cruising at hum speed, I'd hit a pothole or rock in the road. That would skip the vibrate phase and trigger the shakes without warning.
- If I slowed down, it would stop.
- If I nailed it and got past the upper range (bounce barrier) before parts started flying off, it would stop.
- If I increased the tire pressure, the shaking wouldn't start until a much higher speed was reached.
- If I decreased the tire pressure, the shaking pretty much ceased completely. It also made my already unimpressive mileage plummet even worse.
- The easiest solution turned out to be turning or changing lanes. During any turn, the front wheels travel a different distance than the rear wheels and from each other. This brought them out of sync (for a while) and stopped the resonance.
How this may relate:
You mentioned a 20" wheel/tire package.
What kind of tires? Are they strictly highway or are they of a more aggressive nature?
They don't need to have fist sized lugs to resonate.
Let me know if my description sounds/feels like what you're experiencing. If so, forward make/model of your tires. I can check for similar occurrences, histories and most importantly, other solutions.
Hope this will help