Verschiebung-order lower-bound conjecture for finite unipotent group schemes

Let $k$ be a field of positive characteristic, and let $G$ be a finite commutative unipotent group scheme over $k$. Let $V:G^{(p)}\ifinner\ifinner\ifinner\ifinner\ifinner\ifinner\ifinner\ifinner\to\else\longrightarrow\fi\else\longrightarrow\fi\else\longrightarrow\fi\else\longrightarrow\fi\else\longrightarrow\fi\else\longrightarrow\fi\else\longrightarrow\fi\else\longrightarrow\fi G$ be the Verschiebung, and let $n_V(G)$ be the minimal integer $n\ge 1$ such that $V^n=0$. Verschiebung-order lower-bound conjecture.

$$\operatorname{ed}_k(G)\ge n_V(G).$$

This is proposed as a generalization of Ledet's conjecture for finite unipotent commutative group schemes. The supplied text gives no resolution, so the conjecture remains open in this record.