The vote opens the possibility of strikes over Easter, although union sources have previously played down the prospect of any April walk-out.
The ballot was a re-run of an invalid vote held before Christmas.
The row began about cost-cutting but now centres on travel concessions taken from striking staff and disciplinary action against Unite union members.
The latest ballot - the fourth in less than two years - saw 5,811 Unite members vote in favour of strike action, while 1,170 voted against. The turnout was 72%.
The union now has 28 days to announce any strike dates.