Smoothing conjecture and degree bound for Fano threefolds with cDV singularities

Let $V$ be a Fano threefold with only cDV singularities. A smoothing means a deformation whose nearby fibers are smooth.

cDV smoothing conjecture. $V$ has a smoothing by a small deformation. In particular,

$$-K_V^3\le 64.$$

The source notes that the general bound $-K_V^3\le 72$ is not sharp in the cDV case and expects the stronger bound $64$; the proposed smoothing statement is presented as a realistic conjecture.