From the being rebuild Nonohana District, one could take a boat ride northeast to the Hakuren District, then a horse ride north, followed by another boat ride northwest to Kozan District. However, this route was unnecessarily complicated, as a single horse ride from Nonohana District through Gekko District would also reach Kozanami District.
One might argue that the longer route was due to the adventurers' bliss of passing through the mountains of Hakuren District, where rumors of red, human-eating cannibals existed. However, Lucien and Shoji knew the truth – these cannibals were merely fictional creatures from children's fairy tales.
The real reason Lucien and Shoji avoided the shorter route was the presence of Yurei's female members in the Gekko District. Shoji begged to avoid a confratation with his girlfriend, since it would lead to weird suspicions, and Lucy was left with no choice but to agree.