The equivariant Weiss calculus homotopy-category comparison conjecture

Let $\Gmr$ be a finite group and let $\upalpha$ be an indexing representation. Let $\Ecal_{\Gmr, {\bf 0}}^{\Sigma, {\sf conn}}$ be the category of connected-at-infinity equivariant Weiss functors, and let $\widehat{{\bf Sys}}^{\upalpha}_{\sf unif}$ be the category of uniformly bounded-below $\upalpha$-systems with a naive action of $\Omr(\upalpha)$. Write ${\bf Ho}(-)$ for the homotopy category. Homotopy-category comparison conjecture. The homotopy categories are isomorphic:

$${\bf Ho}(\Ecal_{\Gmr, {\bf 0}}^{\Sigma, {\sf conn}})\cong {\bf Ho}(\widehat{{\bf Sys}}^{\upalpha}_{\sf unif}).$$

This comparison would provide the model-categorical equivalence needed to identify the derivative of the $\upalpha$-homogeneous layer with the corresponding derivative of the original equivariant Weiss functor. The source gives no evidence that the conjecture has been resolved.