Wreath Macdonald norm conjecture

Let $\boldsymbol{\boldsymbol{\boldsymbol{\boldsymbol{\lambda}}}}$ be an $[?]$-multipartition and let $[?]$ denote its underlying partition. For a node $[?]=(a,b)[?]$, define its arm length, leg length, and hook length by

$$a([?])=[?]_{b}-a, \qquad \ell([?])=\boldsymbol{\boldsymbol{\boldsymbol{\boldsymbol{\lambda}}}}^{\mathsf T}_{a}-b, \qquad h([?])=a([?])+\ell([?])+1.$$

Wreath Macdonald norm conjecture. The wreath Macdonald polynomials satisfy

\langle P_{\boldsymbol{\boldsymbol{\boldsymbol{\boldsymbol{\lambda}}}}^{*},P_{\boldsymbol{\boldsymbol{\boldsymbol{\boldsymbol{\lambda}}}}}\rangle_{q,t}=\prod_{\substack{\square\in\boldsymbol{\boldsymbol{\boldsymbol{\boldsymbol{\lambda}}}}\\ h(\square)\equiv 0\,\operatorname{mod}\ell}}\frac{1-q^{a(\square)+1}t^{\ell(\square)}}{1-q^{a(\square)}t^{\ell(\square)+1}}.

This is a natural wreath generalization of the Macdonald norm formula and has been confirmed by computations of Orr and Shimozono, but the source does not state a proof or definitive resolution.