Commutativity of the truncated category O and KLR Grothendieck-group diagram

Suppose $\mathfrak{g}$ is simply-laced, let $\lambda\in P_+$, let $\mu\in \operatorname{wt}(V(\lambda))$, and choose an integral set of parameters $\mathbf{R}$ of level $\lambda$. Consider the top quotient $(\mathcal O_\mu^\lambda(\mathbf{R}))_{\operatorname{top}}$, the top Borel–Moore homology group of the repelling affine-Grassmannian slice, the KLR Grothendieck group, and the maps $\psi_\lambda$, $\operatorname{CC}_{\operatorname{top}}^{\tilde X_-}$, $\Theta_{\operatorname{cyc}}$, $\gamma$, and ${\Dbar}^{-}$ shown in the source diagram. Top-level commutativity conjecture. The diagram

\begin{tikzcd}[column sep=1.5em] \operatorname{H}_{\operatorname{top}}\big((\overline{\mathcal{W}}{}^\lambda_\mu)_-\big)\arrow[dr,"\psi_\lambda"'] & K_0((\mathcal O_\mu^\lambda(\mathbf{R}))_{\operatorname{top}}) \arrow[l,"\operatorname{CC}_{\operatorname{top}}^{\tilde{X}_-}"'] \arrow[r,"\Theta_{\operatorname{cyc}}"] & K_0(R_{\lambda-\mu}^\lambda\,\text{-}\,\operatorname{mod})\arrow[dl,"\gamma"]\\ & {\mathbb C}[N]_{-(\lambda-\mu)} & \end{tikzcd}

is commutative. This extends the main theorem's commutative diagram after passing to the top quotient; the source presents it as an expected extension, and no resolution is stated.