Rowmotion-equivariant bijection for minuscule doppelgänger pairs

Let $(P,Q)$ be a minuscule doppelgänger pair, and let $\mathcal{PP}^{m}(P)$ and $\mathcal{PP}^{m}(Q)$ denote their bounded plane-partition sets. Minuscule doppelgänger rowmotion conjecture. There is a bijection

$$\mathcal{PP}^{m}(P)\longleftrightarrow\mathcal{PP}^{m}(Q)$$

which commutes with rowmotion.

The case $m=1$ was proved by Dao, using a bijection of Hamaker and collaborators; the conjecture remains open for general $m$.