I did get an offer to stay here at New Job U. another year. This is good news, more or less because not getting an offer would have been terrible news. My department chair kindly noted that the decision to retain me was not only immediate but also unanimous. That’s good to know.
After learning this, I e-mailed the search chair at Sucktown U. to inform the committee that I had an offer that will expire on April 13. She responded very quickly (on a Friday night, no less) to give me a very detailed account of what their decision timeline will be. Further, she promised that I would likely have an answer at least a few days before the kill date for my current offer. I’m taking this as a good sign, although it likely means nothing other than the SC chair is a courteous professional.
If S-town U. does give me an offer in the next 12 days, it might allow me to see what develops with Farflung U. Or not. Who the hell knows?! This whole process is at once exhilarating and completely draining.