Finite generation of Torelli and IA_n homology modules

Let $\mathcal{I}_{n,1}$ be the Torelli group of a genus-$n$ surface with one boundary component and let $\operatorname{IA}_n$ be the IA-automorphism group of the free group of rank $n$. Their rational homology groups carry actions of $\operatorname{Sp}_{2n}\mathbb{Z}$ and $\operatorname{GL}_n\mathbb{Z}$, respectively. Unstable finite-generation conjecture. For each $i\geq 1$ and each $n\geq 1$, $H_i(\mathcal{I}_{n,1};\mathbb{Q})$ is a finitely generated module over $\operatorname{Sp}_{2n}\mathbb{Z}$, and $H_i(\operatorname{IA}_n;\mathbb{Q})$ is a finitely generated module over $\operatorname{GL}_n\mathbb{Z}$. The conjecture concerns the full, potentially infinite-dimensional homology representations, extending the preceding stable finite-dimensionality proposal; the source gives no resolution.