On the downbeat
Sounds like you need a titanic ice-breaker to turn things around, but I think you need an air of optimism too. If staff are unhappy, it will be reflected in their moods towards each other. Get them together and make them see how silly some of their grievances are, and make a big point of any real grievances. You may find that in those they share some common ground. I would try to build unity out of that. And if that means a few days on the picket line, why not?