Abreu–Diwan–Jackson–Labbate–Sheehan constituent conjecture for pseudo 2-factors

Let $G$ be an essentially $4$-edge-connected pseudo $2$-factor isomorphic cubic bipartite graph, where essentially $4$-edge-connected means 3-edge-connected with no non-trivial 3-edge-cuts. Abreu–Diwan–Jackson–Labbate–Sheehan's constituent conjecture. Then $G\in\{K_{3,3},H_0,P_0\}$. This is one of the two constituent statements whose validity is equivalent in the survey to the preceding 3-edge-connected classification conjecture.