This seems to be a case where the intended driver is one with limited experience. If this were a dedicated drag car I'd say the sway bar isn't that important. Since the driver is a young woman learning to drive, I'd do everything I could to make the car easier to control. Sway bars front and rear, wider tires for better grip, front disc brakes and a long winded tutorial about dealing with old cars!
I hate the thought of a daughter of mine losing control of a car that I bought for her. No room for short cuts here.