The odd-parameter pretzel knot strong quasipositivity conjecture

Let $K=P(\epsilon_1p_1,\ldots,\epsilon_np_n)$ be the pretzel knot under consideration, where each $p_i$ is odd, and let $d=\epsilon_1+\cdots+\epsilon_n$.

Odd-parameter pretzel conjecture. The knot $K$ is strongly quasipositive if and only if either $|d|=n$, or $|d|=n-2$ and, after possibly reordering so that $\epsilon_1=\cdots=\epsilon_{n-1}=+1$ and $\epsilon_n=-1$, one has $p_n<\min\{p_1,\ldots,p_{n-1}\}$.

The source proves the asserted characterization in the cases $|d|=n$ and $|d|=n-2$, and proposes it for all odd parameters; the remaining cases are therefore open there.