Kühn–Osthus conjecture for strongly 2-connected regular digraphs

Let $G$ be a strongly $2$-connected $d$-regular digraph on $n$ vertices, where

$$d\geq n/3.$$

Kühn–Osthus conjecture. The digraph $G$ contains a Hamilton cycle. The source introduces this as the digraph analogue of the $t=2$ case of the Bollobás–Häggkvist conjecture; no resolution is given in the supplied text.