Duality conjecture for strongly pigeonhole classes of matroids

Let $\mathcal{M}$ be a strongly pigeonhole class of matroids. Duality conjecture. The class $\{M^{*}\colon M\in\mathcal{M}\}$ is strongly pigeonhole. The preceding result establishes the analogous claim for pigeonhole classes, but the strongly pigeonhole case is left open.