Nearly unperforated Cuntz semigroups of Z-stable C*-algebras

Let $A$ be a $\mathcal{Z}$-stable $C^*$-algebra, meaning that $A\cong A\otimes\mathcal{Z}$. Let $\operatorname{Cu}(A)$ be its Cuntz semigroup, and recall that a positively ordered semigroup is nearly unperforated when its near-unperforation comparison property holds. Nearly unperforated conjecture. The Cuntz semigroup $\operatorname{Cu}(A)$ is nearly unperforated. This is motivated by the established almost-unperforation results for $\mathcal{Z}$-stable algebras and by partial results under additional hypotheses such as simplicity or real rank zero with stable rank one. The supplied text leaves the general assertion open.