A more fundamental issue is that you're getting scared when the car steps out or spins. That causes a lot of behavior that creates a spin in the first place. Jerky steering, tensing up, abrupt throttle, etc. At an autocross you are in no danger from a spin. The car won't flip over and explode. Relax. When the car starts to oversteer DO NOT lift off the throttle. Stay in the gas and use very quick hands to catch the oversteer and drive through the corner with the back end out a bit.
Toe change is really not the issue. The problem is weight transfer. By lifting off the throttle you're moving weight forward, off the rear wheels, which reduces rear grip. You're car is behaving exactly as it should and is doing what you're telling it to do. By lifting off the throttle when the car is oversteering it you're telling the car to spin. If the back end starts to step out, stay in the throttle and drive through the corner with the back end out a bit.