Gauge-coaction normality conjecture for reductions to amenable groups

Let $(G,P)$ be a WQLO group, let $\Lambda$ be a finitely aligned $P$-graph, and suppose $(G,P)$ reduces to an amenable group. A gauge coaction is the coaction on a representation of $\Lambda$ arising from its $P$-grading.

Gauge-coaction normality conjecture. Every gauge coaction on a representation of $\Lambda$ is normal. Consequently, the other results in the relevant section should require only that $(G,P)$ reduces to an amenable group, rather than the stronger hypothesis that it strongly reduces to an amenable group.

This conjecture would remove the strong-reduction hypothesis from the subsequent results. The paper identifies the normality of gauge coactions as the remaining bottleneck, but the supplied text gives no resolution.