[GeneBob]

I have a 1930 Tudor and installed an anti-sway bar from a late model Crown Vic in the rear to reduce the oversteer. I blamed the higher center of gravity of the sedan body in the back half of the car. It was really only a problem when I started driving the Model A after driving my modern cars. You need to drive the Model A a little different; (or put in the anti-sway bar).
Of course, this assumes that your front and rear suspension are in good working order.