I have had head shake at 25-35 mph on my Roadstar/Champion bike w/ezsteer since new. With 22k on my second Dunlop, I installed a Michelin Commander rear tire on the front. The head shake has disappeared.
The Michelin sidewalls seem to be a lot stiffer than the Dunlop rear I had been running.
I thought this bit of info might help someone with the same issue.