Minkowski difference conjecture for type A MV polytopes

Let $Q$ be an MV polytope of type $A$, and let $Q(\theta_I)$ denote the Schubert matroid polytope associated with $I\subseteq [n]$. For collections $\mathcal{C}_1,\mathcal{C}_2\subseteq 2^{[n]}$, let $a_I$ and $b_I$ be positive numbers. Minkowski difference conjecture. There exist $\mathcal{C}_1$ and $\mathcal{C}_2$ such that

$$Q=\sum_{I\in\mathcal{C}_1}a_IQ(\theta_I)-\sum_{I\in\mathcal{C}_2}b_IQ(\theta_I).$$

This proposes that every type $A$ MV polytope can be expressed as a Minkowski sum and difference of Schubert matroid polytopes, extending the preceding characterization of Minkowski sums that are MV polytopes; the conjecture is presented without a resolution in the source.