There is one very significant factor in all of this regarding bump steer that no one else has mentioned.
That is 1) you can't eliminate all of the bump steer, just reduce it.
2) the stiffness of the tires sidewall is a major factor in what you feel through the steering wheel.
The most dramatic change would be going from the bias tires to a radial tire.
Even so, when you change the profile from the original Michelin's with a 78 profile down to probably what a wide body car would be with 10" wide front wheels, a 35 or 40 profile, even though those are radials, you are stiffening the wall of the tire AGAINST flexing. That is the point of the profile change.
That is going to negate the road shock absorption the tire provides and you will feel more of the shock through the steering wheel of the bump steer.
The Michelin tire that you are using is essentially a race tire legal for street use. That is even STIFFER in the side walls providing even less side wall flex and giving "greater road feel".
The TIRE selection you made is LIKELY the largest contributing factor to the change you are feeling in the steering.
So really this is one of the tradeoffs that you will need to endure.
There just isn't going to be a perfect solution but I go back to my original suggestion, particularly with the wide body cars. You can DAMPEN the shock in the steering wheel by installing an EPS system.
To me, that is the simplest solution and the most effective. Occam's Razor.