Bipartite analogue of the Jaeger–Zhang conjecture

Let $p$ be a positive integer, and let $\mathcal{P}^*_{4p}$ denote the class of signed bipartite planar graphs with the indicated girth condition. Bipartite analogue of the Jaeger–Zhang conjecture.

$$\chi_c(\mathcal{P}^*_{4p})\leq \frac{4p}{2p-1}.$$

This is a modified bipartite analogue of the Jaeger–Zhang conjecture, proposed in light of a later result cited by the paper. The surrounding discussion treats it as an open conjecture and notes related expected bounds for neighboring indices.