The cross brace on my 03 Spyder was very rusty from the exhaust heat. Pulled it off and sand blasted, painted with ceramic header paint.
Noticed that the holes for the bolts were about 3x the diameter needed (easy fitment?).
This meant that the bolts held the plate in place with tension, not the best way. I cut some eccentric spacers out of hardened washers to take up the slack in the holes. The movement of the plate now put the bolts in shear. Much better.
Later I was working under the car with it up on jack stands, when I bumped into a jack, and it moved. After cleaning my shorts, I realized that the car was sitting solid on 3 stands, with the 4th not holding due to the floor being unlevel. The chassis did not flex to allow it to sit on all 4 stands.
I'm not saying that my spacers made the chassis that stiff, but I do believe it helped.
Edit: Without getting too deep into the weeds, Chassis flex and cowl shake are 2 different things that can be interrelated. Many factors such as suspension spring rate, tire traction and the natural (base harmonics) frequency of the chassis determine how much or little cowl shake a car may have. Our cars seem to suffer from a divergent harmonic. Not one that is self damping.