Row-column mirror symmetry for y-ified colored HOMFLYPT homology

Let $P^y_{\boldsymbol{\bigl.\lambda}}$ be $y$-ifications of the categorified projectors $P_{\lambda}$. For an $r$-component link $\mathcal{L}=\mathcal{L}_1\sqcup\dots\sqcup\mathcal{L}_r$, let $HHH^y_{\lambda_1,\dots,\lambda_r}(\mathcal{L})$ denote the resulting $y$-ified colored HOMFLYPT homology, where $\lambda_i^t$ is the transpose partition of $\lambda_i$. Row-column mirror symmetry conjecture. These homology theories satisfy

$$\operatorname{dim}\bigl(HHH^y_{\lambda_1,\dots,\lambda_r}(\mathcal{L})\bigr)(A,Q,T)=\operatorname{dim}\bigl(HHH^y_{\lambda_1^t,\dots,\lambda_r^t}(\mathcal{L})\bigr)(A,T,Q).$$

This conjecture predicts that transposing every coloring exchanges the $Q$- and $T$-gradings while preserving the $A$-grading. It is the proposed mirror symmetry for the $y$-ified colored HOMFLYPT homology package; the source does not provide evidence of a resolution.