[motto]

I understand John that you have had enough of this vexing problem and would like to hear no more on the subject but your point 6 'New tyres made a MAJOR improvement' begs the question. What is it about new tyres that made the difference? The improvement was not only with new tyres but was also experienced with a previous wheel change.
I will quite understand if you don't wish to respond to this post and the last thing I want is to engender any ill feeling but unless I've missed something I believe that you could have possibly achieved the same result with a dynamic (on vehicle) balance. Some vehicles are more tolerant of imbalance than others but on a 20" wheel my experience tells me that balance can be important. Imbalance sometimes having a similar effect to a buckled wheel even at comparatively low speeds. My suggestion that you drop the rear drive shaft and spin up the front wheels one at a time would have shown any imperfection immediately. The violence when this is done can be quite startling and can commence at surprisingly low speeds. Tyre out of round can do this even if balanced.
If balance is irrelevant then about the only explanation I can think of would be a variation in flex or stiffness at different points in the tyre. Very difficult to determine.
I have no wish to start an argument or upset anyone but would sure like to pinpoint the reason for the improvement elusive and all as it may be.

Yours sincerely

David