Low speed shake or wobble in front eng smooths out as you gain speed....

i don't know. you might consider switching front tires
to see if that helps. also try rear wheels for testing.
unlikely but perhaps by moving a rim from 12 to 6 position [ or similar] on rotor may have very small effect.

Sounds like a wheel out of balance,tire low on air, tire belt shifted (starting to go), loose wheel, bad wheel bearing. press the helpful button and check links below
Diagnosing And Repairing Wheel Vibration

Shakes and Wobbles

First check the tire-pressure, then the fork oil; see if the wheel has a loose bearing play.

Speed Wobble - When The Bike Shakes Its Head - Cycling ...

cyclingtips.com.au/2011/.../speed-wobble-when-the-bike-shakes-its-head...

Speed wobble is the term used to describe a quick oscillation of the handlebars ... 2 A scenario seen relatively often is that the top tube of the bike is under-built.

Road Bike High Speed Wobble 1st person view ( Shimmy ...

? 1:27
www.youtube.com/watch?v=hMNFS2ap3fU

Jun 23, 2014 - Uploaded by Aurimas Petraitis
Road Bike High Speed Wobble 1st person view ( Shimmy ) .... causing my bike to be so twitchy on descents ...

How old are the good tires? These speeds usually mean belt or balance problem with tires...If new tires, they need to be re-checked for balance...and not out of round...also check for bent wheel...due to chuckhole? Sometimes a bent steel wheel can be hammered straight...hope this helps.

Jack it up and shake the wheel if it wobbles then it's a bad wheel bearing, if it doesn't then your tire may need to be balanced.

There is a TSB for the PCV hose. The elbows at both ends get holes in the underside that you can't see unless you remove them and look. This is a very, very common issue on the ZX2. You can get a new PCV hose with both elbows for about $30 from the Ford dealership. You only need to remove the air intake to gain access to the PCV hose to replace it.

This is caused by the front disk brake rotors being warped from heat and running out of true, the wobble of the warped rotors causes the wheel to shake when you apply the brakes, it is worse the higher the speed you apply them at. Have the front rotors machined flat again or just replace them.

Does your steering wheel wobble at parking lot speeds, or your ****. If either, you have a bad tire, have it checked ASAP. (if steering wheel wobbles its a front tire.)

could be a bd axle or ball joints wheel bearings are also a concideration

Hi,
There can be a few issues going on that will cause this.
(1) Bad wheel bearings
(2) Warped rotors
(3) Bent front rim

First thing to do is get the bike up on the center stand, or bike jack so the front end is off the ground. You may need someone to push down on the rear to get the front tire off the ground.
Grab the tire and try to move it side to side. If you feel movement, then you will need to have the bearings replaced.
Next rotate the tire and watch for wobble in either the wheel, or the rotors. The shop that replaced the tire should have noted a rim problem when they balanced the tire if that was the issue.
Warped rotors will give a very pronounced wobble at low speeds, and more of a vibration at higher speeds, and it will be most noticeable when braking.
If you have run into anything with any force lately, you may have a bent front axle. I'm assuming that is not the issue.
...word of advice...find a good bike mechanic. Most auto mechs have no clue when it comes these Goldwings.
Hope this helps...Ride Safe...Have Fun