Existence of an HK-realizing principal groupoid with prescribed K-theory

Let $\mathcal{G}$ be a second countable, étale, principal, minimal, ample groupoid. A groupoid $\widetilde{\mathcal{G}}$ is required to have the same listed properties, and $K_*(C^*_r(\mathcal{G}))$ denotes the $K$-theory of the reduced groupoid $C^*$-algebra.

HK-realization conjecture. There should exist a possibly different groupoid $\widetilde{\mathcal{G}}$ such that

$$K_*(C^*_r(\mathcal{G})) \cong K_*(C^*_r(\widetilde{\mathcal{G}}))$$

and the HK-conjecture holds for $\widetilde{\mathcal{G}}$.

This question asks whether every $K$-theory group arising from a principal minimal ample groupoid can also be realized by one satisfying the HK-conjecture. The source presents it as a question motivated by positive results, and gives no resolution.