Another thought, albeit a somewhat longer shot.
Do you feel the car rolling across the front axle , when the instability starts? The unloading of the inside wheel can cause it go "light" and not maintain good contact with the road.
If this is the case the only method I know to minimise roll is to fit an SSL front end kit , when properly adjusted there is almost no perceptible roll, the front wheels stay more upright in cornering and there is a benefit to ride quality as well.
