Do you run wheelie bars? You may need to. More weight on the nose may be needed as well, considering you can carry the fronts in the air that far.
I know little about caltracs, but can say this; if you have a car set up with the I C too low, it can aggravate wheelstands. the reason is with an I C below the neutral line it wants to instantly drop the rear and lift the front. You say the front tires don't turn, that was my clue.

I made a major change in my car, going from 50/50 to 53front/47rear weight distribution and the car settled right down and allowed the wheelie bars to control the wheel stands without unloading the back tires.
The main thing about moving that much weight is you may need to hit the tire harder to achieve weight transfer, but you will have enough torque to maintain traction so the car won't care how much weight is moved forward.