Are your rear shocks set to factory recommendations for your weight and load? If not, the rear can steer the front. My '10 SESG which is identical to yours in all relative aspects, is rock solid at 80+ in corners marked 60. And, stable on the freeway in bursts well above 90mph.
Can you give us any clues about how the rear shocks can cause this condition? I'm running a pair of aftermarket rear shocks and would like some idea of how they might be adjusted to cure a condition like this.
My '10 CUSE has wobbled or weaved in ~80 mph sweepers so I took it to my stealership and they charged me $115 to tighten the head bearings. And it's still under warranty!!

After doing a little research on this site, I found an H-D bulletin that came out in '09 that talked about correct head bearing adjustment. I think it said that head bearings that are too tight can inhibit the bike's ability to absorb a weave, and too loose can inhibit it's ability to fight a wobble. It didn't give any clues as to how to define a weave or wobble though. It sounds important to know which problem you are faced with.
I'm thinking my bike may have a weave, which means my dealer did exactly the wrong thing to fix it -and they charged me for it too!