Cranston–Rabern's strong-coloring conjecture for vertex-transitive graphs

Let $G$ be a vertex-transitive graph with maximum degree $\Delta$, and let $s\chi(G)$ denote its strong chromatic number, the smallest $r$ such that every partition of $V(G)$ into parts of size $r$ admits a proper coloring using all $r$ colors on each part. Cranston–Rabern's strong-coloring conjecture. The strong chromatic number of any vertex-transitive graph is at most

$$s\chi(G) \leq \frac52\Delta.$$

This is introduced as an intermediate conjecture toward the strong $2\Delta$-colorability conjecture; the supplied source gives no resolution.