Piśniak's distinguishing-index conjecture for 2-connected graphs

Let $G$ be a simple connected graph. Its distinguishing index $D'(G)$ is the least number of labels in an edge labeling preserved only by the identity automorphism. Write $\Delta(G)$ for its maximum degree.

Piśniak's conjecture. If $G$ is a $2$-connected graph, then

$$D'(G)\leq 1+\lceil \sqrt{\Delta(G)}\rceil.$$

This conjecture gives a substantially sharper upper bound for the distinguishing index of 2-connected graphs than the general maximum-degree bounds discussed in the paper. The supplied text does not state whether it has been resolved.