How to keep plans for a job change quiet?
This is common in academia. I think you have to be honest with everyone who might rely on you being at your current job in the future, let them know what stage you are at, and ask them to keep it to themselves until you get the official offer. You can only control what you say to others while asking others to respect your privacy in the meantime. 

Suppose that you told everyone in your current department exactly what you have told us, and for some reason your new position falls through at this late date, what's the worst case situation you're worried about? It seems to me that, assuming your current job is held for you, your worst problems will be interpersonal with other faculty that resented your desire to leave. Is that it, or are you worried about some specific ramifications if word got around?