First, consider that wind has real HIT. Odd things happen to two wheel vehicles in wind.That is weird, I never would have thought that bars or mirrors would affect handling that much. Makes me think some motorcycles are not manufactured properly and are at the edge of stability. For what its worth, I have been chasing a slight wobble on my Thruxton ever since new. All the changes (tires, steering damper, shocks, fork springs & oil, steering head tapered bearings) I have made do help but when I get on a windy highway @ about 130 KMH the wobble sometimes returns. Maybe I need to change the bars?
Second, one thing that is sorely overlooked and has been for a while is wheel alignment front to rear. Not chain alignment, WHEEL alignment. I've too many bikes where the front and rear wheels are not aligned.
Having the chain straight between countershaft and rear sprocket does not mean that the front wheel is aligned to the rear. The result of that misalignment is often blamed on tires, steering head bearings, and other stuff.
Really want to induce a wobble... install a luggage rack with a top box and hold on for dear life at speed.