Covering gonality bound for Gorenstein unicuspidal rational curves

Let $C$ be a Gorenstein unicuspidal rational curve of genus $g$, and let $\gon_F(C)$ denote its covering gonality, namely the smallest degree of a map from $C$ to $\mathbb{P}^1$. Covering gonality conjecture.

$$\gon_F(C)\leq\left\lceil\frac{g+1}{2}\right\rceil.$$

This proposes a uniform upper bound for the covering gonality of Gorenstein unicuspidal rational curves. The supplied text gives no evidence that the bound has been proved or disproved.