Conjecture on cyclically 4-edge-connected cubic graphs attaining cycle covering ratio 7/5

Let $G$ be a cubic graph. Its cycle covering ratio is the minimum length of a cycle cover divided by $|E(G)|$. A cubic graph is cyclically $4$-edge-connected if no edge cut of size less than $4$ separates two subgraphs each containing a cycle.

Cyclic 4-edge-connectivity conjecture. Up to isomorphism, the Petersen graph is the only cyclically $4$-edge-connected cubic graph with cycle covering ratio $7/5$.

The conjecture is motivated by known infinite families attaining the ratio $7/5$, all with cyclic connectivity $2$ or $3$. Its status is open.