The rigged-configuration bijection for type D KR crystals

Let $B=B^{r_1,s_1}\otimes B^{r_2,s_2}\otimes\cdots\otimes B^{r_L,s_L}$ be a tensor product of Kirillov--Reshetikhin crystals, and let $\operatorname{RC}(B)$ be its set of rigged configurations. The map $\Phi$ constructs a tensor product of rectangular tableaux, identified with an element of $B$. The bijection conjecture. The map $\Phi$ gives a bijection

$$\operatorname{RC}(B)\longrightarrow B.$$

This is the basic conjecture underlying the proposed filling map from rigged configurations to KR tableaux; the supplied text does not state whether it has been proved or disproved.