The spanning subdivision conjecture for digraphs under non-edge degree-sum conditions

Let $H$ be a digraph with minimum degree $\delta(H)\geq 1$. Let $D$ be a digraph of order $n$, and for vertices $u,v\in V(D)$ with $uv\notin A(D)$ consider the degree-sum condition $d_D^+(u)+d_D^-(v)\geq n+C_H$.

Spanning subdivision conjecture. There is a constant $n_0$ and a real number $C_H$ depending only on $H$ such that, whenever $D$ has order $n$ and the displayed condition holds for every non-edge $uv$, $D$ contains a spanning $H$-subdivision.

This is posed as a problem for sparser digraphs than those covered by the main dense-digraph results. The source gives no resolution of this proposed statement, so its status remains open.