I just thought of something I've tried in the past. Not sure how violent the shake is, and sounds like this new dealer may have things under control.
But have you tried having someone else drive your car and you follow and look things over as the car is moving.
I've had my wife drive the car and my brother drive me in another car. We would drive next to, behind, and in front of the car and look for problems like yours. Sometimes you can see what's going on better when driving next to the car rather than sitting in it.
Just a thought, you never know what'll work.
Has this worked for anyone else?
When I have problems like this, like most of us, I try process of elimination. I think of anything that would spin or cause shake.
Wheel bearings (front and back), brake rotors (calipers) - all of these items could be checked by the hand feel for heat method we discussed earlier.
Front end and rear end suspension components (bushings). Usually grabbing a wheel and shaking can disclose.
Stearing components (would show up as uneven tire wear quickly).
Crappy tires, actually had bad pair of goodyears cause this problem once for me.
Then drive train
Like you say, not space shuttle, not rocket science.