The wheels-part characterization of the multivariable Alexander polynomial

Let ordinary links be regarded as w-links, and let $Z$ be the associated invariant whose target is a diagram space. Quotient the target by the “Commutators Commute” relation, and consider the wheels part of $Z$.

Wheels-part Alexander conjecture. What remains of the wheels part of $Z$ is precisely the multivariable Alexander polynomial.

This identifies the Alexander polynomial as the information carried by the wheels part of the universal invariant after imposing the stated commutativity relation. The source presents the claim without giving a resolution.