The Seifert-surface identification conjecture for knot Floer homology

Let $K$ be a knot in $S^3$ and let $R$ be a genus $g$ Seifert surface of $K$. Write $\widehat{HFK}(K,g)$ for the top Alexander-graded knot Floer homology and $\operatorname{SFH}(S^3(R))$ for the sutured Floer homology of the sutured manifold obtained by decomposing $S^3$ along $R$. Seifert-surface identification conjecture. There is an isomorphism

$$\widehat{HFK}(K,g) \approx \operatorname{SFH}(S^3(R)).$$

Together with the vanishing result for non-taut sutured manifolds, this would imply the vanishing of $\widehat{HFK}(K,g)$ above the three-genus and would provide a new proof of nonvanishing in the top Alexander grading.