Two spanning temporal arborescences under half-connectivity

Let $N=((V\cup s,A),\tau)$ be an acyclic temporal network on $n\ge 4$ vertices. For vertices $s,v\in V\cup\{s\}$, let $\lambda_N(s,v)$ denote the maximum number of arc-disjoint $\tau$-respecting $(s,v)$-paths, and let a spanning $\tau$-respecting $s$-arborescence be a spanning arborescence rooted at $s$ whose root-to-vertex paths respect the temporal ordering.

Two-arborescence conjecture. If

$$\lambda_N(s,v)\ge \frac n2$$

for every $v\in V$, then $N$ contains a packing of $2$ spanning $\tau$-respecting $s$-arborescences.

This would improve the preceding sufficient condition $\lambda_N(s,v)\ge n-1$ for packing two spanning temporal arborescences. The conjecture is presented as an open strengthening for acyclic temporal networks; no resolution is given here.