Stressed-hyperplane relaxation conjecture for Ehrhart positivity

Let $M$ be an Ehrhart-positive matroid, meaning that the coefficients of its Ehrhart polynomial are nonnegative, and let $H$ be a stressed hyperplane in $M$. Write $\operatorname{Rel}_H(M)$ for the matroid obtained by relaxing $H$.

Stressed-hyperplane relaxation conjecture. If $M$ is Ehrhart positive and $H$ is a stressed hyperplane in $M$, then $\operatorname{Rel}_H(M)$ is also Ehrhart positive.

This is presented alongside the panhandle positivity conjecture and is supported by substantial computational evidence. Its resolution status is not specified in the supplied text.