Virtual combinatorial R-matrix conjecture for KR crystals

Let $B^{r,s}$ and $B^{r',s'}$ be KR crystals of type $D_4^{(3)}$, and let the virtual combinatorial $R$-matrix be induced by restriction of the type $D_4^{(1)}$ combinatorial $R$-matrix through virtualization. Virtual R-matrix conjecture. The virtual $R$-matrix is well-defined on

$$B^{r,s}\otimes B^{r',s'}.$$

Well-definedness would extend the virtual $R$-matrix construction from the cases already understood in the paper to arbitrary pairs of KR crystal factors.