I've got a stock windscreen on mine. The plain Jane straight up one. Never had a wobble on mine at up to 120 MPH. Perhaps that upward curve at the top is inducing some kind of turbulence.

 

Road Glide FTW!

 

Wobble comes from two areas.

The first, is you have a front linkage, a top linkage, but no third point linkage in back to hold the drive line (engine/trans/rear swing arm/rear tire) that is all one piece that is not actually bolts to the frame (just rubber isolators). so rear tire torque, or even side torque to the rear end in a corner, will allow rapid changes to the drive line at the rear tire, to move withing the frame that is isolated from. Hence rear end wobble.


The second form of wobble, can happen back up at the head seat that can cause handle bar slap, and this is from the fairing causing the front end to lift (in bikes like the ultra's, back end to be pushed down) at speeds to cause the front end to be lighter/less pressure to the road.

In the case of rear end wobble, all kinds of ways to add in a third link or extra isolator stiffeners to hold the back end of the drive line solid to frame.

In regards to front end, something like fork fangs that will push the front end down from wind pressure against them, go a long way to resolve the front end lift head shake problems.

Bottom line, this is not rocket science, and just comes down to if your trying to use the bike as a touring road bike and minimize vibration to the frame, or if trying to use the bike for strip use, where you don't want the stock isolators in play alone, but more ridgid ways of holding the drive line straight in line with the frame isntead.
Note, neither are going to work for a high speed standing 1 mile runs, since your talking of speeds over 130MPH and in territory that HD never aerodynamic designed the bikes to run in the first place.

 

Is this the same as the death wobble for 30 years ago, that some said Harley should have recalled touring bikes?

Key is a shot of kessler before getting on the bike to loosen up your grip.

 

I’ve bought four HD touring bikes in the past four years. I ride about 1000 miles a month. Less than some, more than some.

I live in NC where the speed limit is 70MPH or less, so I typically pass at 90mph or less. 95 if I’m feeling saucy.
I might ride into to TN, VA and SC. Speed limits same I think.

No wobble.