Incommensurability conjecture for fully augmented pretzel and rotated links

Let $FALP_n$ and $FALP_m$ denote the fully augmented pretzel links with the indicated numbers of regions, and let $FALR_n$ denote the corresponding rotated fully augmented link. Two hyperbolic link complements are incommensurable when they have no common finite-sheeted cover.

Incommensurability conjecture. The following assertions hold:

$$FALP_n\text{ and }FALP_m\text{ are incommensurable for }n\ne m.$$

For $n\geq 4$,

$$FALP_n\text{ and }FALR_n\text{ are incommensurable for all }n.$$

The claim concerns commensurability distinctions among the link complements studied in the paper. The supplied text proves commensurability of the family $FALR_n$ with one another, but gives no resolution of these two incommensurability assertions.