Giordano's spectral-sequence collapse conjecture for twisted polynomial superfunctors

Let $d,r\geq 0$, let $\mathcal{P}_d$ be the degree-$d$ strict polynomial functor category, let $\mathbfcal{P}_{dp^r}$ be the corresponding superfunctor category, and let $F,G\in\mathcal{P}$. Consider the spectral sequence

$$\boldsymbol{II}_{F,G,r}^{s,t}:=\operatorname{Ext}_{\mathcal{P}_d}^s\bigl(F,\textbf{R}^t\rho(G_0^{(r)})\bigr)\Rightarrow\operatorname{Ext}^{s+t}_{\mathbfcal{P}_{dp^r}}(F_0^{(r)},G_0^{(r)}).$$

Spectral-sequence collapse conjecture. For all $F,G\in\mathcal{P}$, this spectral sequence collapses at the second page. In particular, there is a graded isomorphism, not necessarily natural,

$$\operatorname{Ext}^*_{\mathbfcal{P}_{dp^r}}(F_0^{(r)},G_0^{(r)})\simeq\operatorname{Ext}^*_{\mathcal{P}_d}(F,G_{\boldsymbol{E_{r}}}).$$

The collapse would identify the twisted Ext-spaces with the Ext-spaces of the untwisted functors after parametrisation by $\boldsymbol{E_r}$. The source gives no evidence of a resolution, so the conjecture remains open.