Existence conjecture for genus-detecting higher-order Alexander torsion

Let $K$ be a knot. Genus-detecting higher-order torsion conjecture. There exists an epimorphism $\gamma\colon\pi_K\to\Gamma$ onto a torsion-free elementary-amenable group such that

$$\deg\bigl(\tau(K,\gamma)\bigr)=2\operatorname{genus}(K)-1.$$

This would provide a higher-order Alexander torsion attaining the sharp genus bound for every knot. The source gives no resolution.