I have a 1990 FLHTCU with 64K on it. At speeds under 75mph it is perfectly stable. At speeds over 75mph (even a few miles over) the front end ever so slightly "wallows" left and right. I can feel it in the handlebars and I can see the fairing rocking left and right.
Its scary.
Lots of guys are installing steering stabilizers but I am thinking its worn out swingarm bushings. I am looking at the Rivera Primo Stiffey replacement bushings. They look super easy to install and they only cost $100.00. Also.. they seem to address the problem more correctly and factory than adding a steering stabilizer or brace.

 

I have a 09 FXSTC with 55,000 miles on it , had the high speed wobble problem, changed neck bearings, wheel bearings, tires, nothing seemed to help, so at last resort I drained the oil out of the lower legs into a measuring cup, and low and behold it had about 3 oz. to much.. so I replaced the oil with just 9 oz. cause it wasn't all the way dry I figured... and it fixed the wobble.. all I can think is, when the bike was in for pre paid service at the dealer they put to much oil in there when they changed it..... it sure gave me alot of head aches, cause I love to lay into a curve ....

 

I am by no means a speed freak on my RK but when i first got the bike and rode two up for a while the rear end felt loose, almost as if the rear would want to go sideways after hitting a bump or taking a fast curve. I fitted the progressive touring stabilizer link and was amazed at the difference. It was almost as if the rear wheel was part of the bike!!! The ride is now tight and predictable and really should have been this way when it left the factory.

 

Same here, never felt a wobble.

 

Dads brand new 09 Deluxe wobbled during high speed turns and sometimes during straight aways. Harley took the front end apart, realigned everything etc, etc. Nothing fixed it, so they gave him a good deal for trade in and bought a 2010 Heritage Softtail and hasn't had any wobble problems at all.....

 

I hear a lot of "back off the throttle" in a front end high speed wobble. DON'T decel too fast, DON'T brake. Move your butt forward and onto the gas tank and decel slowly. The weight shift will help stabilize the wobble.

 

You could try lowering the rear a half inch, sounds like you need more trail. It fixed my 2004 road king.