Simon’s genus monotonicity conjecture for knot-group epimorphisms

Let $J$ and $K$ be knots with knot groups $\pi_J$ and $\pi_K$, and let $\varphi:\pi_J\twoheadrightarrow\pi_K$ be a surjective homomorphism. Simon’s genus monotonicity conjecture. Their genera satisfy

$$g(J)\geq g(K).$$

This is attributed to Problem 1.12 in Kirby’s collection of problems. The source records studies of surjective homomorphisms of knot groups and explains that a suitable representation detecting the genus could establish the conjecture, but gives no resolution.