Adding to what the others have already shared and some more:
The wobble can be a number of things and they're common to all motorcycles: tire condition, tire pressure, steering head bearing wear and preload and even suspension settings.
I was recently on the phone with Marty and she said that they had one that was the result of a worn shock. A new shock fixed it right up. There's another data point for you.
Back to the steering head bearings because they're obviously where you'd start (right after tire condition and pressure). As it sounds like you're aware, the bearings on most big bikes need a little bit of preload to create some drag in the steering. My old Honda GL1200 Gold Wing specified that with the tire in the air, the bearings needed enough preload that with a fishing scale on the end of the handlebar, it took 14-18 oz (roughly a pound) of force to get the bars to start moving. If you think about that, it's quite a bit. Under that amount and the Gold Wing would have the same death wobble.
To get at them, you'll need to obviously get the bike up on some kind of center stand or lift. Unlike a normal bike, the second you remove the fork crown, the front end is going to collapse unless you have the weight safely supported.
Please for the love of all that is holy, remove the tank before doing this job. There's too much stuff clanging around that can damage it. Remove it now.
- Remove the four handlebar pinch screws, lift the bars off and try to set them somewhere they won't dent the headlight bucket or front fender (towels and tape to hold them everywhere).
- Under there are two 1/4-20 screws with tiny hex sockets. 50/50 chance of stripping the head and needing to drill these off.
- Slide the handlebar risers off to reveal the riser studs. Remove them.
- Remove the brake hose clamp screw on the front of the fork crown. This becomes important after the next step.
- Remove the chrome acorn nut. I have personally found that a large adjustable wrench and a paper towel over the nut are far kinder here than attempting to use a socket.
At that point, the top crown should be free enough to hinge away from the upper nut and bearings. Or--if you prefer--you can remove the 1/4-20 socket head cap screws on the top of the struts and remove the whole thing.
From there, it's an obvious double-nut arrangement. The thing I'd share there is: it's hard to tighten the bearing and have a wrench thin enough to hold it while trying to also snug up the jam-nut.
To make this step easier,
the answer is a hydraulic wrench. They are thinner than standard open-end spanners. Sorry, I don't remember the dimension of the nut. The wrench I bought on ebay is a Proto and it's a double-ended, 1-3/16, 1-1/4". From the marks on the wrench, I'm inclined to say it's the 1-1/4" side that fit but, I can't swear to that.
After fighting with the adjustment once and still not getting it right, I made sure I had the wrench for the next go-around. Picture from ebay attached. There happens to be one loose wrench for $19.99 that I got that pic from.
Assembly is reverse of removal.