Homotopy hypothesis for strict non-unital n-groupoids

An $n$-snugroupoid is a recursively defined strict, non-unital $n$-groupoid, and an $n$-truncated space is a space whose homotopy groups vanish above degree $n$. Write $\Pi_n$ and $\Re$ for the proposed functors between these categories, and localize the category of $n$-snugroupoids at equivalences and the category of $n$-truncated spaces at weak equivalences.

Homotopy hypothesis for snugroupoids. There are functors

$$\Pi_n\quad\text{and}\quad\Re$$

between the categories of $n$-snugroupoids and $n$-truncated spaces, in the usual directions, together with adjunction morphisms inducing an equivalence between these two localizations.

The author reports that an argument of Kapranov and Voevodsky may prove the statement, but explicitly says that this has not been checked, particularly concerning identity elements; its status is therefore left open.