Torisu's unknotting-number-one conjecture for Montesinos knots

Let $K$ be a Montesinos knot of length three. Write $\mathcal{M}(0;(p,r),(q,s),(2mn\pm1,2n^2))$ for the Montesinos-knot notation used in the source, where $p$, $q$, $r$, $s$, $m$, and $n$ are non-zero integers, $m$ and $n$ are coprime, and $ps+rq=1$.

Torisu's conjecture. The knot satisfies $u(K)=1$ if and only if

$$K=\mathcal{M}(0;(p,r),(q,s),(2mn\pm1,2n^2)).$$

Torisu proved this equivalence when the unknotting operation is realised in a standard diagram, but the unrestricted statement is presented as a conjecture; it would follow from the Seifert fibering conjecture described below.