The high-speed shakes whilst driving and braking

Whilst pelting around on a 'race track' in excess of 100 mph, the steering wheel shakes and moves a little. This also happens when braking at high speeds but is much more noticeable. I am aware that the surface of the 'race track' is not entirely flat and so the wobble may come from that and also that wind buffeting will shake the car a little too. Is there anything that can be done to eliminate this shake? I have googled the same question and seen suggestions such as upgrading or simply replacing suspension bushings, getting tyres balanced and even buying new rotors. Some say it's just old suspension that judders, some say uneven tyre wear and others say it's brake dust not evenly disappating from the rotors. Any thoughts or suggestions as to how I can eliminate this? I've already got stiffer springs waiting to be installed which will tighten things up a little
 
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