Bounded-distance crossings conjecture for quasi-transitive 1-planar graphs

Let $G$ be a quasi-transitive graph of bounded degree with a plane embedding in which every edge has at most one crossing. For crossing edges $uv$ and $xy$, let $d_G$ denote graph distance.

Bounded-distance crossings conjecture. There is an integer $k$ such that for every pair of crossing edges $uv,xy$ in $G$, we have

$$d_G(u,x)\leq k.$$

The source states that this conjecture would directly imply the quasi-transitive 1-planar coarse-planarity conjecture, and hence the bounded-crossing conjecture. Its resolution status is not specified.