X=M conjecture for type D4^(3) KR crystals

Let $B$ be a tensor product of KR crystals of type $D_4^{(3)}$, and let $\mathcal{P}(B;\lambda)$ denote its classically highest weight elements of classical weight $\lambda$. Define the one-dimensional sum and fermionic formula by

$$X(B,\lambda;q)=\sum_{b\in\mathcal{P}(B;\lambda)}q^{D(b)},$$ $$M(B,\lambda;q)=\sum_{(\nu,J)\in\operatorname{RC}^{HW}(B;\lambda)}q^{\operatorname{cc}(\nu,J)}.$$

X=M conjecture. One has

$$X(B,\lambda;q)=M(B,\lambda;q).$$

This predicts equality between the energy-generating one-dimensional sum and the cocharge-generating fermionic formula for all tensor products of type $D_4^{(3)}$ KR crystals.