It’s not happening on my one ... Make sure your wheels are correctly balanced and your tyres are in a good condition and shape ... there could be many other things that could affect high speed driving ..... You could check the suspension front and rear if everything is tight .. GS is rock solid I agree.. but is not getting even near to the MTS performance..
There was something up with that bike... I got rid and got a 2017 1200S Multi that is much better, but it's still not 100% stable compared to the GS. For sure the Multi is "faster" but with me as the limiting factor I'm as fast point to point on the GS or XR as I am on the MTS. I do find that when cracking on the MTS is not stable above 130mph and when gassing it hard I can get a good weave on. I know that the bike is right as it can be, and the Road 5 tyres are tyres I gel with... it's just a twitchy bike at speed. Great on warm twisty French roads though... And that was fully-laden!
I have always been a steering damper fan, I fit them on every bike I ride. I am aware they do not 'fix' issues only mask them, but I am happier to have a bike in a straight line at 100mph plus even if it is 'masked' by artificial means. I have not done many miles on my Multi, but I did pick up that it is light on the front at speed, its to be expected really with wide bars and me being a fat bast. I also genuinely prefer a heavier steering setup anyway. I was going the multistrada enduro steering damper way, but the German seller discovered he didn't have what he thought he had when I ordered it, so now I am waiting on a Ducabike/Ohlins setup to arrive. Its what the rider likes IMO, some like specific tyres, some like firm suspension, some like different tyre pressures - I like a steering damper and the confidence it gives me. The Ducabike setup is ugly as sin - but then I am no great shakes either lol I will keep my lid on if the steering damper keeps me in a straight line and everyone is happy
My DVT in touring has had a little shimmy over 100 with a top box on an open road With a bit of cross wind but hasn’t without a top box or in sports mode, a simple gentle back off of a few mph will stop it
When I had my ZX10R, it was my mission in life never, ever, ever, EVER to be beaten by anything with a top box ... ...now I have a bike with topbox and panniers so it's OK