The quotient-stack and ordinary blowup isomorphism compatibility conjecture

Let $X$ be a smooth projective variety with a $G$-action, let $Z\subset X$ be a $G$-invariant submanifold of codimension $c\geq 2$, and set $\widetilde X=\operatorname{Bl}_Z(X)$ and $X'=X\sqcup Z\sqcup\cdots\sqcup Z$ with $c-1$ copies of $Z$. Let $iso_{[\widetilde X/G],[X'/G]}$ be the partial quotient-stack isomorphism and $iso_{\widetilde X,X'}$ Iritani's isomorphism for the ordinary A-model. Blowup isomorphism compatibility conjecture. The partial isomorphism from the preceding conjecture coincides with the restriction of Iritani's isomorphism $iso_{\widetilde X,X'}$ to the loci of $G$-fixed points. This compares the quotient-stack blowup correspondence with the corresponding correspondence after forgetting the group action; the source gives no resolution status.