Wu–Xu–Xu conjecture on 3-colorability of even-hole-restricted graphs

For an integer $\ell\geq 2$, let ${\cal H}_{\ell}$ denote the family of graphs with girth $2\ell$ and no even holes of length at least $2\ell+2$.

Wu–Xu–Xu conjecture. Every graph in $\bigcup_{\ell\geq 2}{\cal H}_{\ell}$ is $3$-colorable.

This is the even-hole analogue of the resolved conjecture for the families ${\cal G}_{\ell}$. The source presents it as a proposed conjecture and gives no resolution.