Semistable form of Grinenko's dP3 rigidity conjecture

Let $X\to\mathbb{P}^1$ be a semistable $dP_3$ fibration with nonsingular total space, in the sense cited by the source, and suppose it satisfies condition $(\ast)$:

$$-K_X\notin\operatorname{Int}\operatorname{\overline{NM}}^1(X).$$

Semistable dP3 rigidity conjecture. Then $X/\mathbb{P}^1$ is birationally rigid. This is a semistable variant of Grinenko's conjecture.