Weakly strong Neuwirth conjecture for prime non-torus knots

Let $K$ be a prime non-torus knot, let $F$ be a non-orientable spanning surface for $K$, and let $E(K)$ be the exterior of $K$. The surface $F\cap E(K)$ is required to be geometrically incompressible and boundary incompressible. Weakly strong Neuwirth conjecture. For any prime non-torus knot $K$, there exists a non-orientable spanning surface $F$ for $K$ such that $F\cap E(K)$ is geometrically incompressible and boundary incompressible. The paper introduces this as a weakening of the Strong Neuwirth conjecture and states that it is also unknown.