Asymptotic volume conjecture for cusped orientable hyperbolic 3-manifolds

For each positive integer $n$, let $v_n$ be the minimal volume of an $n$-cusped orientable hyperbolic $3$-manifold. Let $V_8$ denote the volume of the regular ideal octahedron.

Asymptotic volume conjecture.

$$\lim_{n\to\infty}\frac{v_n}{n}=V_8.$$

This predicts the asymptotic minimal volume per cusp. The source notes the lower bound $v_n/n\geq V_3$ due to Adams, but gives no proof of the asserted limit.