Indecomposable-module conjecture for Euler characteristics of crepant resolutions

Let $k$ be an algebraically closed field of characteristic $p>0$, and let $G\subseteq \mathrm{SL}(n,k)$ be a finite small group of finite representation type, meaning that there are finitely many isomorphism classes of indecomposable $kG$-modules. Let $P$ be a $p$-Sylow subgroup of $G$. Suppose that both

$$X:=\mathbb{A}^n_k/G$$

and

$$X':=\mathbb{A}^n_k/P$$

have crepant resolutions $f:Y\to X$ and $f':Y'\to X'$. Indecomposable-module conjecture. Then

$$e(Y)=\#\mathrm{Ind}_k(G).$$

This conjectures that the number of isomorphism classes of indecomposable $kG$-modules gives the algebraic invariant corresponding to the Euler characteristic of a crepant resolution in positive characteristic. The result is motivated by the main theorem for groups with a non-modular abelian normal subgroup of index $p$, while the assertion remains open in the stated generality.