A single covariance sign change in random orientations of $G(n,m)$

Let $G(n,m)$ be the uniformly random graph with exactly $m$ edges on $n$ vertices, and orient every present edge independently and uniformly at random. Fix distinct vertices $s,a,b$, and let $A$ be the event that there is no directed path from $a$ to $s$, while $B$ is the event that there is no directed path from $s$ to $b$. The covariance in question is

$$\operatorname{Cov}(\mathbf{1}_A,\mathbf{1}_B)=\mathbb{P}(A\cap B)-\mathbb{P}(A)\mathbb{P}(B).$$

Single-sign-change conjecture. For any fixed $n\ge 5$, the covariance in $G(n,m)$ changes sign only once between two values of $m$.