Oriented (2,4,4)-flows double-cover conjecture

Establish that every bridgeless graph, or at least every bridgeless cubic graph, has an oriented (2,4,4)-flows double cover, consisting of three subgraphs carrying nowhere-zero 2-, 4-, and 4-flows whose edge orientations cover each edge in both directions.

Background

The paper relates ordinary (2,4,4)-flows to 6-cycle 4-covers and asks whether the flow decomposition can be equipped with compatible orientations. The conjecture is trivial for 3-edge-colourable cubic graphs and was computationally verified by the paper for small snarks up to 28 vertices, but no general proof is given.