As I recall, the elliptical wing planform is not the whole answer. This is off the top of my head without any research.

The Spitfire, to my recollation also had an elliptical cross section such that the pressure distribution reduced or stopped the outflow. the problem with this is the great difficulty of construction with all the compound curves in the wing.

What I am saying is that you just can't use an elliptical plan form, you must also have an elliptical spar for the full effect. Try covering this with aluminum. This is one reason why this type wing wasn't extensively used.

An improved version of the same basic airframe design was the Spiteful which had a straight tapered, laminar flow wing.