Car goes sideways?

Remember that the driveshaft spins counterclockwise ( viewed from the back) and tries to lift the right tire. The sure grip clutches lock in and since the left tire is not spinning yet, it has more traction. This upsets the balance of the car and since the right tire (which is spinning) it is easier to drag it sideways. This all takes place in a split second and the if you are able to get both tires spinning, the back end always seems to want to go to the low side.

You're 100% right Dave...and this is the main reason for relocating the battery to the right rear corner of the trunk - to use the added weight to help counteract the lifting of the right rear tire.
Years ago, the combination of battery relocation, adjustable pinion snubber, and SS springs kept my NHRA Super Street (10.90 index) '69 Dart launching straight and hard.
15 years later and I still wish I hadn't sold that car.