Akiyama–Watanabe–Albertson–Hass conjecture for bipartite planar graphs

Let $G$ be a bipartite planar graph, and let $\mathrm{fvs}(G)$ denote the minimum size of a feedback vertex set of $G$, that is, a vertex set whose deletion leaves a forest.

Akiyama–Watanabe–Albertson–Hass conjecture. Every bipartite planar graph $G$ satisfies

$$\mathrm{fvs}(G)\leq \frac{3v(G)}{8}.$$

The source describes this as an open conjecture. The current best bound given there is $\mathrm{fvs}(G)\leq (3v(G)-3)/7$, which does not establish the conjectured bound.