Was reading an old post about this and thought I would start a fresh one to detail some things I've learned (mostly by luck) about front wheel wobble on my Silverwing and my Vespa GTS.
Silverwing has always had the coast-down wobble around 30 mph. Research on the Internet convinced me to live with it, because it is so common on bikes. Late last year it showed just a trace of wobble at high speeds (50 mph +). Both tires (Diablos) had about 6500 miles on them, and the rear was worn out. I had a new rear tire installed, but kept the front because it looked very good still. Wobble seemed worse after the new rear tire was installed (and balanced).
HyperPro springs were installed about 500 miles later. The wobble was still there. I tried rear shock settings from 1 to 5 without any effect. I usually ride without a top box. It got worse all summer as I added miles. Finally, the front tire was worn enough that I got it replaced (with a Metzeler) a month or so ago (front Diablo lasted about 10,000 miles). The wobble has immediately disappeared. Maybe because the Metzeler is fabulous, but probably because it is NEW and still has the proper profile (as opposed to a worn out, flattened old tire).
Vespa GTS's are known for a coast down wobble. I got mine used, with a new Diablo on the rear and the stock tire (a SAVA - generally held in low regard). Initially it had no wobble. As the tires wore out, it began to wobble somewhat. Two months ago I got two brand new Michelins installed (and balanced) and got a dreadful wobble as soon as I drove away.
I tried adjusting the rear shocks, adding heavier bar end weights, riding with and without a box (usually without), shifting my weight from front to back. Nothing helped. Then I experimented with air pressure (tire placard says 26/29 psi front/rear). Nothing changed with more air in back. I added air to the front tire (37 psi) and the wobble almost entirely went away. It will wobble a tiny bit, then stop by itself. If I drop the front to 32 psi, the wobble starts to come back. My guess is that the original tires have very stiff sidewalls, and the Michelin City Grips have softer sidewalls. The addition of air pressure probably stiffens the side wall of the tire.
I don't feel any rocking or looseness in the steering or wheel bearings on either bike. Shocks are stock (Vespa just hit 8000 miles and the Silverwing has 18,000 miles), with the exception of the HyperPros on the Swing. I've come to the conclusion that wobble is going to come and go, mostly driven by the amount of wear on the tires and especially by the wear on the front tire. My Silverwing front tire still had one mm of tread in the center, but should have been tossed months ago.
If you've got the $$$, install front and rear tires whenever you need either tire. If you've got some wobble, try adding air to the tires (esp. the front) above and beyond what Honda recommends (but not over the max limit on the sidewall of the tire).
Hope this post saves somebody from a headache.