As people have said before, no one is doubting that a heavier car will be harder on the drive train. And I certainly am not doubting your expertise, skill, or experience, all of which are clearly far above mine.
But F=MA isn't a robust explanation for the higher shock loads. By saying that F increases with M, you assume that A remains constant. This would undermine the advantage of bringing a lighter car to the track.
The force that breaks drivelines isn't the required force to accelerate the car, but the maximum applied torque before the tires lose grip. This is defined not by the weight of the car necessarily but by the weight on the rear tires. The traction of the tires has a positive, but not necessarily 1:1 linear relationship with the weight loading on the them.
Picture a Z with 1000lbs of lead directly on top of or in front of the front axle. It would require no more force for this Z to spin its tires than a standard Z, and thus would be no harder on the drive train.
A Z with 1000lbs directly on the rear axle would have significantly more traction as well as a higher traction to overall weight ratio. As a result the required force to spin the tires would be higher and thus it would be harder on the driveline.
just food for thought....