Defective list edge-colouring conjecture

Let $G$ be a graph and let $d$ be an integer. Write $ch'_d(G)$ for the $d$-defective list chromatic index and $\chi'_d(G)$ for the $d$-defective edge chromatic number.

Defective list edge-colouring conjecture. For every graph $G$ and every integer $d$,

$$ch'_d(G)=\chi'_d(G).$$

This is a stronger defective analogue of the list edge-colouring conjecture; the source says it is proved for bipartite graphs, while the general assertion remains open.