Pessimistic assumption: At least in the limit of unusually thin and long objects, Transfiguration time actually scales as the product of the shortest local dimension with the square of the longest local dimension of the target, rather than the volume. Harry has not detected this because he was always Transfiguring volumes or areas, and McGonagall was mistaken.
In Azkaban is stated that Harry transfiguration of a thin cylindrical layer from the wall is fast because its volume is small. This seems to contradict your assumption.
Pessimistic assumption: At least in the limit of unusually thin and long objects, Transfiguration time actually scales as the product of the shortest local dimension with the square of the longest local dimension of the target, rather than the volume. Harry has not detected this because he was always Transfiguring volumes or areas, and McGonagall was mistaken.
In Azkaban is stated that Harry transfiguration of a thin cylindrical layer from the wall is fast because its volume is small. This seems to contradict your assumption.