The higher-girth packing conjecture for strongly planar digraphs

A feedback vertex set of a digraph is a set of vertices whose deletion leaves an acyclic digraph, and a strongly planar digraph is a digraph arising from an oriented plane graph with a perfect matching as described in the paper. Let $D$ be a strongly planar digraph of girth $g$.

Higher-girth packing conjecture. There exists a packing of $g$ pairwise disjoint feedback vertex sets in $D$. Equivalently, $D$ can be vertex $g$-coloured such that every directed cycle uses each colour at least once.

The case $g=3$ gives the known $2$-colourability result for strongly planar digraphs, and the directed cycle of length $g$ shows that the proposed bound is best possible. The general statement remains open.