Rich flows for 3-edge-connected graphs

Let $G$ be a $3$-edge-connected graph, meaning that deleting fewer than three edges does not disconnect it, and let its maximum degree be $\Delta$. A rich $k$-flow is a nowhere-zero $k$-flow whose absolute values differ on every pair of adjacent edges.

Rich-flow conjecture for 3-edge-connected graphs. Every $3$-edge-connected graph with maximum degree $\Delta$ admits a rich $(\Delta+3)$-flow.

This conjecture would substantially improve the paper's general linear bound for the more highly connected case. The source presents it as a belief, and no resolution is given.