Armstrong's rank and co-skew-length symmetry conjecture for coprime cores

Let $a$ and $b$ be relatively prime positive integers, and let $\kappa$ range over all $(a,b)$-core partitions. Write $\operatorname{rk}(\kappa)$ for the rank, and define the co-skew length by

$$\operatorname{sl}'(\kappa):=\frac{(a-1)(b-1)}{2}-\operatorname{sl}(\kappa).$$

Armstrong's rank and co-skew-length symmetry conjecture. The following $q,t$-polynomials are equal:

$$\sum_{\kappa}q^{\operatorname{rk}(\kappa)}t^{\operatorname{sl}'(\kappa)} = \sum_{\kappa}q^{\operatorname{sl}'(\kappa)}t^{\operatorname{rk}(\kappa)},$$

where both sums are over all $(a,b)$-cores $\kappa$. This conjecture predicts a symmetry exchanging rank and co-skew length in the joint enumeration of coprime core partitions; the source gives no resolution status.