The collapsing conjecture for twisting spectral sequences

Let $F$ and $G$ be strict polynomial functors, and for $r\geq 0$ let $E(F,G,r)$ denote the twisting spectral sequence associated with them, whose abutment computes ${\mathrm{Ext}}^*(F^{(r)},G^{(r)})$. Collapsing conjecture. For all $r\geq 0$, and all $F,G$, the twisting spectral sequence $E(F,G,r)$ collapses at the second page. The conjecture would explain why known computations exhibit equality between the total dimensions of the twisted Ext groups and the corresponding second-page terms, even without an evident lacunary argument; whether this collapse always occurs remains open.