Bang-Jensen et al.'s tightness conjecture for the cycle-transversal bound

Let $\tau(D)$ denote the minimum size of a vertex set whose deletion makes an oriented graph $D$ acyclic, and let $\operatorname{inv}(D)$ denote its inversion number.

Bang-Jensen et al.'s tightness conjecture. For every positive integer $n$, there exists an oriented graph $D$ such that

$$\tau(D)=n\quad\text{and}\quad\operatorname{inv}(D)=2n.$$

The conjecture asserts that the general bound $\operatorname{inv}(D)\leq2\tau(D)$ is tight for every positive value of the cycle-transversal number; the paper notes it would follow from the dijoin conjecture. The source does not state a resolution.