Finite-rank crystal-graph comparison conjecture for finite unitary groups

Let $t$ be a non-negative integer, set $r=t(t+1)/2$ and $\iota=r\pmod 2$, and let $\widetilde{\mathcal{G}}_{\iota,q,\ell}^{t,\leq d}$ be the induced subgraph of the reindexed Harish-Chandra branching graph on vertices of rank at most $d$. Let $\mathcal{G}_{\mathbf{c},e}^{\leq d}$ be the corresponding crystal graph truncated at rank $d$. Graph-comparison conjecture. Assume that $e$ is odd and put $\mathbf{c}=(t+(1-e)/2,0)$. Then there is an integer $b=b(\ell)$ such that

$$\widetilde{\mathcal{G}}_{\iota,q,\ell}^{t,\leq b}=\mathcal{G}_{\mathbf{c},e}^{\leq b},$$

when the colouring of the edges of the latter graph is ignored. This conjecture predicts that, up to a bound depending on $\ell$, the relevant Harish-Chandra branching graph agrees with a crystal graph after reindexing. The source gives no resolution.