Unbounded separation between orbital chromatic and chromatic roots

Let $N>0$. A graph $\Gamma$ has chromatic polynomial $P_{\Gamma}(x)$, and let $G$ be an automorphism group of $\Gamma$. The orbital chromatic polynomial $OP_{\Gamma,G}(x)$ is the polynomial associated with the action of $G$ on $\Gamma$.

Unbounded separation conjecture. For any $N>0$, there exists a graph $\Gamma$ and automorphism group $G$ of $\Gamma$ for which $OP_{\Gamma,G}(x)$ has a root at least $N$ larger than the largest real root of $P_{\Gamma}(x)$.

This conjecture asks whether orbital chromatic roots can lie arbitrarily far to the right of the largest real chromatic root. The paper notes that orbital chromatic roots can exceed chromatic roots, but gives no resolution of whether their separation is unbounded.