James, the wing design was set in 1934, Mitchell’s interest in the elliptical wing stems from a flying boat project (of his) of 1929 ,a six engined monster designed to ministry specification 20/28.

After BS Shenstones visit to the US, the NACA 2200 aerofoil section was adopted, but the single main spar arrangement from the flying boat was retained, (consideration was given to the idea that the main spar may be bent to the elliptical shape of the wing, but Supermarine thought it impossible to bend the spar through 2 axis, and in doing so, would remove the obvious datum point of the wing, further complicating the design) the position of the single mainspar dictates the chord of the wing ,and the U/C pintle is mounted directly to that, therefor the wheels retract into the deepest part of the wing.

If the laminar flow principle was known about, at that time (or indeed after) ,to incorporate it would not only mean a complete redesign of the wing aerofoils, but also the main spar position and the way in which the U/C retracted,the position of the guns etc, together with a new attatchment point on the fuselage ; you could say a complete A/C .

I would suggest that either the laminar flow concept had not been discovered in 1934, or else the details of it were kept secret, by all accounts it was (the NACA 2200 series) at that time, the wing shape with the lowest induced drag ; it is possible, however, for the wing to be laminar and elliptical.