Conant's integral Conway polynomial splitting conjecture for amphicheiral knots

Let $K$ be an amphicheiral knot, and let $C_K(z)$ denote its Conway polynomial. Conant's integral splitting conjecture. For some $\phi\in\mathbb Z[z]$, one has

$$C_K(z)=\phi(z)\phi(-z).$$

The conjecture strengthens the mod-4 splitting claim and is already known for negative and strongly positive amphicheiral knots by the Hartley–Kawauchi theorem. It is refuted by the same counterexamples of Ermotti, Hongler, and Weber that disprove the mod-4 claim.