Conjecture on valid orientations for two specified faces

Let $G$ be a plane graph with a valid prescription function $p:V(G)\rightarrow\{-1,0,1\}$, two specified faces $F_G$ and $F_G^*$, and at most one specified vertex $d$ or $t$. If $d$ is present, it is an oriented vertex of degree $3$, $4$, or $5$ on the boundary of one of the specified faces. If $t$ is present, it is a degree-$3$ vertex on the boundary of one of them. Assume

$$G\text{ is 3-edge-connected,}$$

$G$ has at most one $3$-edge-cut, only $\delta(\{d\})$ or $\delta(\{t\})$, and every vertex outside the boundaries of $F_G$ and $F_G^*$ has five edge-disjoint paths to their union.

Conjecture on valid orientations for two specified faces. Then $G$ has a valid orientation.

This removes from the preceding theorem the requirement that the oriented vertex lie on both specified faces and the requirement that the faces have a common vertex. The source presents the assertion as an open extension.