Kidwell–Stoimenow's degree conjecture for Whitehead doubles

Let $K$) be a non-trivial knot, and let $W(K)$ be a Whitehead double of $K$. The Kidwell–Stoimenow conjecture. Is it always the case that

$$\max\deg_z P_{W(K)}-1=2\max\deg_x F_K?$$

Kidwell and Stoimenow reported that the conjecture holds for all prime knots with up to $11$ crossings by exhaustive calculation; its general status is not resolved in the supplied source.