Existence and specialization conjecture for the two-variable augmentation polynomial

Let $K$ be a knot, and let $\operatorname{Aug}_K(\lambda,\mu,U)$ be its three-variable augmentation polynomial. When the $U=1$ slice of the augmentation variety has a maximal-dimensional Zariski closure of codimension $1$, denote its reduced defining polynomial by $\operatorname{Aug}_K(\lambda,\mu)$. Two-variable augmentation-polynomial conjecture. The two-variable augmentation polynomial is always defined, and

$$\operatorname{Aug}_K(\lambda,\mu)=\operatorname{Aug}_K(\lambda,\mu,U=1).$$

This predicts both universal existence of the two-variable invariant and its identification with the $U=1$ specialization of the three-variable augmentation polynomial.