Thanks for posting Gregor, super frustrating I'm sure.
I don't think the frame flexing, shaking all over is causing the wobble it's a result. The tires start wobbling back and forth long before the oscillations get to the mounts and frame. Sure, that stuff needs to be stronger to take the violent oscillations of weight but I think those oscillations start from something independent.
Nothing is mentioned about the brake pads (you did say it starts right after hitting the brakes, I had to replace 1 caliper in the front and I used the new pads in it, old in the other, and it has pulled a little that way ever since)) or alignment settings toe in/out could be adjusted either way easily to test.
It's my theory that it is an outlying issue, all the bracketry, axle, frame, is all the same van to van.
Best of luck, I will be following along, hopefully something gets figured out, lot of these coil kits on the road.