The exterior-algebra module refinement of Némethi's conjecture

Let $G$ be a plumbing tree, let $Y(G)$ be its associated plumbed 3-manifold, and let $\boldsymbol{\mathbf{\mathit{HF}}}^-(Y(G))$ denote the completed Heegaard Floer homology. Write $\operatorname{Tors}$ for the torsion subgroup of $H_1(Y(G))$, and let $\Lambda^* H_1(Y(G))/\operatorname{Tors}$ act through the $H_1(Y(G))/\operatorname{Tors}$ actions on the two theories. Némethi's module-structure conjecture. $\boldsymbol{\mathbf{\mathit{HF}}}^-(Y(G))$ is isomorphic to $\mathbb{HF}(G)$ as a module over

$$\mathbb{F}[[U]]\otimes \Lambda^* H_1(Y(G))/\operatorname{Tors}.$$

This refines the lattice-homology conjecture when $b_1(Y(G))>0$ by requiring compatibility with the exterior-algebra action, beyond the underlying $\mathbb{F}[[U]]$-module isomorphism. The source does not state a resolution of this refinement.