The simple-digraph counterexample conjecture for the fully directed bunkbed model

Let $D$ be a simple digraph. Construct $\widetilde{D}$ by adding both directed vertical edges $v^{(0)}v^{(1)}$ and $v^{(1)}v^{(0)}$ for every $v\in V(D)$, and let $E_8$ select a subset of the edges uniformly at random. Simple-digraph counterexample conjecture. There exists a simple digraph $D$ for which the bunkbed inequality fails:

$$\operatorname{BBC}(E_8,D)\text{ is false}.$$

This conjecture asks whether the counterexample can be made fully directed and simple rather than using multiple edges and undirected vertical edges; the supplied text gives no resolution.