The top-twisted equality conjecture for Jack characters

Let $\pi$ be a partition, let $\lambda$ be a Young diagram, and let $\alpha>0$. Denote by $\operatorname{Ch}_\pi^{(\alpha)}$ the Jack character and by $\widehat{\operatorname{Ch}}_\pi^{(\alpha)}$ the orientability generating series. The top-twisted equality conjecture. The top-twisted parts of these two quantities are equal:

$$\lim_{s\to\infty}\frac{1}{s^{|\pi|+\ell(\pi)}}\operatorname{Ch}_\pi^{(s\alpha)}(s\lambda)=\lim_{s\to\infty}\frac{1}{s^{|\pi|+\ell(\pi)}}\widehat{\operatorname{Ch}}_\pi^{(s\alpha)}(s\lambda).$$

This is presented as a conjectural consequence concerning the highest-degree, or top-twisted, contributions of the Jack character and its orientability generating series; the source gives no resolution beyond the stated assertion.