I have to ask for a clarification
The strut tower brace on top is chassis stiffness (of marginal effectiveness I'll grant) and not the core reason for the handling behavior you describe.
The bars/springs/alignment change the way the car handles - making the base that you attach them to stiffer is only going to make a more consistent framework to measure and effect change. If stiffening the front chassis causes the car to push the primary reason is that the suspension was too stiff for the chassis and flexing in the unibody rather than the spring. Stiffening the chassis (by saaay tying it into the roll cage) allows a much stiffer framework - and allows more aggressive spring/bar rates to be effective. The side effect is (as you have observed) is that it causes fatigue in the still-not-so-stiff areas of the setup.
spedhere: 98 M3 ♣ 90 325i ♣ 01 Tundra V8