Strong version of Ishii's conjecture for the Links–Gould invariant

Let $L$ be an alternating link with $\mu$ components, and write its Links–Gould polynomial as

$$\mathrm{LG}(L;t_0,t_1)=\sum_{i,j}a_{ij}t_0^i t_1^j.$$

For a two-indexed sequence $(a_{ij})$, define its support by $\operatorname{Supp}(a_{ij})=\{(i,j)\in\mathbb Z^2:a_{ij}\ne0\}$; it has no interior zeros when

$$\operatorname{Conv}(\operatorname{Supp}(a_{ij}))\cap\mathbb Z^2=\operatorname{Supp}(a_{ij}).$$

Strong version of Ishii's conjecture. The coefficients satisfy $a_{ij}=(-1)^{\mu+i+j+1}|a_{ij}|$ for all $i,j$, and $(a_{ij})$ has no interior zeros. The source notes that this stronger formulation is false for another two-variable Alexander-polynomial generalization, but gives no resolution for the Links–Gould claim.