The interval-shape conjecture for left-orderable surgery slopes

Let $K$ be a nontrivial knot in $S^3$ that is not a cable of a nontrivial knot, and let $g(K)$ denote its genus. Define

$$\mathcal{S}_{LO}(K)=\{r\in\mathbb{Q}\mid \pi_1(K(r))\text{ is left-orderable}\}.$$

Interval-shape conjecture. The set $\mathcal{S}_{LO}(K)$ coincides with one of

$$\mathbb{Q},\qquad (-\infty,2g(K)-1)\cap\mathbb{Q},\qquad \text{or}\qquad (-2g(K)+1,\infty)\cap\mathbb{Q}.$$

This conjecture is suggested by the known interval structure of $L$-space surgery slopes together with the surgery dichotomy conjecture. Its resolution status is not specified in the source.