Sadly the Electra Glide models are not known for high speed stability, and short of a major redesign I doubt they ever will be. The frame change in 2009 was a huge improvement in terms of greatly reducing rear steer; however, Harley hasn't done a thing to improve the high speed stability of the front end. You still have the front end geometry that Harley came out with decades ago to improve very low speed maneuverability (think cop bikes and parade duty). Back in those days an E'glide didn't have sufficient power to reach triple digit speeds, unless you rode it off a tall cliff.
Anyhow, there are some things that will make the problem worse. Definitely get the steering head bearings properly lubricated and then check the preload of those bearings. There is no steering damper to control oscillations, so you have to depend on the steering head preload to provide some damping. Also have the balance and runout of the front wheel/tire/brake assembly measured. Lateral imbalance and runout can definitely cause a high speed wobble. And don't forget proper tire inflation.
There isn't much you can do to fix the fork mounted fairing problem, short of trading for a Road Glide.
Jerry