Intriguing thread...
I don't think we can completely rule out that the kkim-wobble might be the result of torque-induced precession: when a spinning top slows down the amplitude and frequency of wobbles increases.
There are many sources of torque that have the effect of pushing the wheel to one side, such as a minute amounts of debris rattling a bearing ever so slightly. Now, when you take the wheel off and hold it horizontally and whack it a couple of times when changing the tire the piece of debris dislocates and the problem disappears!
This would easy to check: take the tire all the way off and put it back on as if it were a new one. If that solves the problem, it would save people experiencing wobbles a lot of cash, as it would prove that the new tires are
not an essential part of the solution.
For what it's worth, the following scientific paper has other explanations:
Study of stability of a two wheeled vehicle through experiments on the road and in laboratory