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do the connectors serve to evenly distribute that energy? does it stop the drivers side of the engine from lifting that side of the car? isn't that what is actually causing the body twist?

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What they do is stiffen the car so it distributes the load more evenly.

As far as motor torque, put the car in low and power brake it as high as you can. That is the amount the motor itself is twisting the car. Launch the car and you will see the rest of the effects of the pinion climbing the ring gear, and it's transmission to the rest of the car through the rear springs.