OK, so here is the upshot:
I'm fairly certain that my contract extension was supported by both the FAO and the Dean of our English Department. I had worked with the current head of our FAO on a project three years ago, when he was dean of biology, and we have always gotten along well. In fact, I have asked him to write a letter of recommendation for me, which he did. It says, in part, that “Due to the local policy in Zhejiang Province, a foreigner may not stay in the same school for more than five years.” There is no mention of having to leave China, which is quite a different story from the one I was told initially [by a different person].
The story I get now is that my extension was nixed by a vice-president of the school, and, reading tea leaves, one might suspect that there is some sort of office politics going on. But who knows?