Gras's finiteness conjecture for exceptional primes of dihedral Artin representations

Let $\rho=\operatorname{Ind}_{\operatorname{G}_L}^{\mathbb{Q}}\zeta$ be an odd two-dimensional dihedral Artin representation, with $L$ imaginary quadratic, and let $S(\rho)$ be the set of primes specified in the source. Let $T(\rho)$ be the primes $p\in S(\rho)$ for which the associated Selmer group $S_{\chi,\epsilon}(\mathbb{Q}_\infty)$ vanishes at every prime above $p$, and put $T'(\rho)=S(\rho)\backslash T(\rho)$. Finiteness conjecture. The set $T'(\rho)$ is finite; equivalently, only finitely many pairs $(\mathfrak{p},\epsilon)$ of the stated kind have nonzero associated Selmer group. This is motivated by Gras's p-rationality conjecture and the cited implication from p-rationality to membership in $T(\rho)$; it is open in the source.