Conjecture on flow roots of 3-connected graphs

Let $G$ be a 3-connected graph with $n$ vertices and $m$ edges, and let $F(G,t)$ denote its flow polynomial. Let $\phi\approx1.749$ be the flow root of $K_5$ in $(1,2)$. 3-connected flow-root conjecture.

$$F(G,t)\text{ is non-zero with sign }(-1)^{m-n}\quad\text{for }t\in(1,\phi).$$

If $G$ is not an Eulerian graph with $m-n$ odd, the same conclusion should hold for $t\in(1,2)$. This is the flow-polynomial analogue of the preceding conjecture for 3-connected chromatic graphs; the source gives no proof or resolution.