This doesn't explain why you get the same amount of curl if the stone rotates twice during its run or twenty times.
V_cm: velocity of center of mass
V_l: velocity at left edge
V_r: velocity at right edge
R: radius of stone
w: angular speed of stone (CCW is +)
V_l = V_cm + R*w
V_r = V_cm - R*w
delta = 2*R*w
Even if it was dependent on linear speed / rotational speed, the only way to change # of turns / run is to change linear speed / rotational speed.