Mundy's Arthur multiplicity conjecture for certain G2 representations

Assume $S_0=\emptyset$, where $S_0$ is the subset of $S(\pi_{\mathbf f})$ consisting of places $p$ with $\pi_p={\rm St}_p$. Let $S'\subset S(\pi_{\mathbf f})$, let $\Pi_\infty$ be the specified quaternionic discrete series representation of $G_2(\mathbb R)$, and let $\Pi_p^+$ and $\Pi_p^-$ be the local representations defined in the source. Set

$$\Pi=\Pi_\infty\otimes\bigotimes_{p\in S'}\Pi_p^-\otimes\bigotimes_{p\notin S'}'\Pi_p^+.$$

Mundy's conjecture. The representation $\Pi$ occurs in $L^2_{\rm disc}(G_2(\mathbb Q)\backslash G_2(\mathbb A))$ with multiplicity zero or one, and it occurs with multiplicity one if and only if

$$\epsilon\left(\frac12,\operatorname{Sym}^3(\pi_f)\right)=-(-1)^{\#S'},$$

equivalently, if and only if $\#S'$ is even. This is presented as a special case of an Arthur multiplicity formula. The source subsequently says that, when $C=1$, the conjecture is true, so its status is solved in that case, but does not establish the unrestricted statement beyond that setting.