So, you're on short final at 80 knots, descending at 400-500 feet per minute? When you say "swings a lot" are you saying the nose is moving left and right, up and down, or are the wings rocking a lot? Or all three? What is the wind? What kind of controllers are you using (yoke, joystick...rudder pedals?). Also, have you tried adjusting your control sensitivities?
Gregg