[Trevor Booth]

The gyroscopic action of a wheel only comes into play when you want to change/ move the spinning axis. This force is called precession. precession is the "anti gravitational" or "self righting" force. A car wheel when turned by the steering is rotating about , say, a vertical axis, say, normal to its spinning axis (the stub axle) no gyroscopic force is encountered as the plane (horizontal) of the spinning axis is unchanged, however, in reality, the kpi and castor will promote a slight change in the plane of the spinning axis and some precession will occur. I have really not calculated this but I would suggest that unless speeds are very very high it may not have an effect if at all.
Try the old bicycle wheel held between your hands, it is only when you "lean it over" that any resistance is felt.
BTW when a bicycle rider wants to make a LH turn he actually turns a fraction to the right in order to make the LH turn

The upshot- no i dont believe gyroscopic action contributes to heavy steering at speed