Monotone metric rigidity conjecture for polytopes

Let $P\subset\mathbb{R}^d$ and $Q\subset\mathbb{R}^e$ be polytopes with isomorphic edge-graphs. Assume that $0\in\operatorname{int}(Q)$, every edge of $Q$ is at most as long as its corresponding edge in $P$, and every vertex-origin distance in $Q$ is at least as large as the corresponding distance in $P$. Monotone metric rigidity conjecture. Then $P$ and $Q$ are isometric via an orthogonal transformation. This is presented as a stronger conjecture related to the main reconstruction claim, and the source gives no resolution.