Original tire was a Metzler - shook bad & was cupped excesively. Replaced with an Avon Cobra & shake was better, but not completely gone. wore out the Avon & put on a Michelin commander II - shake is gone
Had a similar problem with new tyres on my old GL1800. New Avons fitted and I had a real bad shake or front end wobble. Took it back and complained vociferously. Had them rebalanced and still the same. Had front swapped for a new tyre - no problem. First tyre was defective in manufacture and it maybe the same here.
I had the same thing happen with a Metz. One day all seemed good. The next ride and the handle bars shook like crazy. 6,000 miles on the front tire. Never got less than 9,000 on a front tire before this or after.