Jon, Mate had dunlops on his new Suzi and although the tyre appeared fine, when you looked at the deep part of the tread in the cut away, you could see the carcass on a couple of 'em and also a couple of bubbles. Wouldn't know to look at it though. New tyres required.
Had exactly the same symptoms with my 999. Shakey wobble through the bars almost exactly at 50mph when travelling at a constant speed or gently decelerating. Tried resetting everything by the book, checked tyre pressures, tread wear, wheel rim damage, compression and rebound front & rear, no change.
A service at Pro Twins and a look at by Rob seemed to cure it somewhat (hint - ignore the handbook for suspension settings, more damping needed than you'd think although you'd expect that as I'm about 17.5 stone all kitted up) with the recommendation that tyre wear, particularly of the front (although there's loads of tread left) linked to a squaring-off of the rear can cause these symptoms. A brand new rear made things better, just have to try a new front soon.
I've never had these symptoms before on any bike, even one with worn tyres and to be perfectly honest it really made me paranoid as the shake feels like it's going to develop into a major tankslapper. Conscious effort was needed to control it - grab those bars tight!