Klein-bottle prism conjecture for hexagonal tessellations

Let $\Gamma$ be a prism of a hexagonal tessellation of the Klein bottle, and suppose its cutout contains an $m\times n$ array of tiles, with $m$ and $n$ even. Assume that both types of colorings of the hexagonal prism described in the surrounding discussion occur. Klein-bottle prism conjecture. The prism is egc, that is, it admits an edge-girth coloring.

This conjecture gives a sufficient parity condition for edge-girth colorability of these Klein-bottle prisms and requires the presence of both local coloring types. The source reports computational evidence in support, but no proof or resolution.