Cichacz–Suchan irregular-labeling conjecture for digraphs

Let $\overrightarrow{G}$ be a digraph of order $n$ whose weakly connected components all have order at least $3$, and let $\Gamma$ be an Abelian group. A $\Gamma$-irregular labeling is a labeling in which the vertex weights are distinct, as defined in the surrounding discussion. Cichacz–Suchan's irregular-labeling conjecture. There exists a constant $K$ such that every such digraph $\overrightarrow{G}$ has a $\Gamma$-irregular labeling for every Abelian group $\Gamma$ satisfying

$$|\Gamma|\geq n+K.$$

This is presented as a conjecture based on bounds previously obtained for components of order at least $4$ and for groups of size greater than $(1+\varepsilon)n$; no resolution is given.